-
1
-
-
85164644063
-
-
I. M. Gel'fand and B. M. Levitan, On the determination of a differential equation by its spectral function, Dokl. Akad. Nauk SSSR (N.S.) 77:4 (1951), 557-560. (Russian)
-
I. M. Gel'fand and B. M. Levitan, "On the determination of a differential equation by its spectral function", Dokl. Akad. Nauk SSSR (N.S.) 77:4 (1951), 557-560. (Russian)
-
-
-
-
2
-
-
0016369301
-
The inverse scattering transform - Fourier analysis for nonlinear problems
-
M. J. Ablowitz, D. J. Kaup, A. C. Newell, and H. Segur, "The inverse scattering transform - Fourier analysis for nonlinear problems", Studies in Appl. Math. 53:4 (1974), 249-315.
-
(1974)
Studies in Appl. Math
, vol.53
, Issue.4
, pp. 249-315
-
-
Ablowitz, M.J.1
Kaup, D.J.2
Newell, A.C.3
Segur, H.4
-
3
-
-
84913921727
-
Non-linear equations of Korteweg-de Vries type, finite-zone linear operators, and Abelian varieties
-
1 (1976, 55-136 Russian
-
B. A. Dubrovin, V. A. Matveev, and S. P. Novikov, "Non-linear equations of Korteweg-de Vries type, finite-zone linear operators, and Abelian varieties", Uspekhi Mat. Nauk 31:1 (1976), 55-136 (Russian);
-
Uspekhi Mat. Nauk
, vol.31
-
-
Dubrovin, B.A.1
Matveev, V.A.2
Novikov, S.P.3
-
5
-
-
85164644871
-
-
B. A. Dubrovin, I. M. Krichever, and S. P. Novikov, Integrable systems I, Dynamical systems IV, Itogi Nauki i Tekhniki. Current problems in mathematics. Fundamental directions, 4, Akad. Nauk SSSR, Vsesoyuz. Inst. Nauchn. i Tekhn. Inform., Moscow 1985, pp. 179-284 (Russian);
-
B. A. Dubrovin, I. M. Krichever, and S. P. Novikov, "Integrable systems I", Dynamical systems IV, Itogi Nauki i Tekhniki. Current problems in mathematics. Fundamental directions, vol. 4, Akad. Nauk SSSR, Vsesoyuz. Inst. Nauchn. i Tekhn. Inform., Moscow 1985, pp. 179-284 (Russian);
-
-
-
-
6
-
-
85164632713
-
-
English transl., Dynamical systems IV. Symplectic geometry and its applications, Encyclopaedia Math. Sci., Springer-Verlag, Berlin 1990, pp. 173-280; 2nd rev. aug. ed., 2001, pp. 177-332.
-
English transl., Dynamical systems IV. Symplectic geometry and its applications, Encyclopaedia Math. Sci., Springer-Verlag, Berlin 1990, pp. 173-280; 2nd rev. aug. ed., 2001, pp. 177-332.
-
-
-
-
7
-
-
36049057587
-
Method for solving the Korteweg-de Vries equation
-
C. S. Gardner, J. M. Greene, M. D. Kruskal, and R. M. Miura, "Method for solving the Korteweg-de Vries equation", Phys. Rev. Lett. 19 (1967), 1095-1097.
-
(1967)
Phys. Rev. Lett
, vol.19
, pp. 1095-1097
-
-
Gardner, C.S.1
Greene, J.M.2
Kruskal, M.D.3
Miura, R.M.4
-
8
-
-
84980193643
-
Korteweg-de Vries equation and generalization. VI. Method for exact solution
-
C. S. Gardner, J. M. Greene, M. D. Kruskal, and R. M. Miura, "Korteweg-de Vries equation and generalization. VI. Method for exact solution", Comm. Pure Appl. Math. 27 (1974), 97-133.
-
(1974)
Comm. Pure Appl. Math
, vol.27
, pp. 97-133
-
-
Gardner, C.S.1
Greene, J.M.2
Kruskal, M.D.3
Miura, R.M.4
-
9
-
-
0000079951
-
A periodic problem for the Korteweg-de Vries equation. I
-
3 (1974, 54-66 Russian
-
S. P. Novikov, "A periodic problem for the Korteweg-de Vries equation. I", Funkcional. Anal. i Priložen. 8:3 (1974), 54-66 (Russian);
-
Funkcional. Anal. i Priložen
, vol.8
-
-
Novikov, S.P.1
-
11
-
-
0009372301
-
A scheme for integrating the nonlinear equations of mathematical physics by the method of the inverse scattering problem. I
-
3 (1974, 43-53 Russian
-
V. E. Zaharov and A. B. Šabat, "A scheme for integrating the nonlinear equations of mathematical physics by the method of the inverse scattering problem. I", Funkcional. Anal. i Priložen. 8:3 (1974), 43-53 (Russian);
-
Funkcional. Anal. i Priložen
, vol.8
-
-
Zaharov, V.E.1
Šabat, A.B.2
-
13
-
-
0005655067
-
Estimates of the stability intervals for Hill's equation
-
H. Hochstadt, "Estimates of the stability intervals for Hill's equation", Proc. Amer. Math. Soc. 14 (1963), 930-932.
-
(1963)
Proc. Amer. Math. Soc
, vol.14
, pp. 930-932
-
-
Hochstadt, H.1
-
14
-
-
33646978170
-
On the determination of a Hill's equation from its spectrum
-
H. Hochstadt, "On the determination of a Hill's equation from its spectrum", Arch. Rational Mech. Anal. 19 (1965), 353-362.
-
(1965)
Arch. Rational Mech. Anal
, vol.19
, pp. 353-362
-
-
Hochstadt, H.1
-
15
-
-
27144541971
-
Asymptotics of the width of gaps in the spectrum of the Sturm-Liouville operator with a periodic potential
-
5 (1974, 1048-1051 Russian
-
V. F. Lazutkin and T. F. Pankratova, "Asymptotics of the width of gaps in the spectrum of the Sturm-Liouville operator with a periodic potential", Dokl. Akad. Nauk SSSR 215:5 (1974), 1048-1051 (Russian);
-
Dokl. Akad. Nauk SSSR
, vol.215
-
-
Lazutkin, V.F.1
Pankratova, T.F.2
-
17
-
-
85164636097
-
-
V. A. Marčenko [Marchenko] and I. V. Ostrovskii, A characterization of the spectrum of Hill's operator, Mat. Sb. (N.S.) 97 (139):4(8) (1975), 540-606 (Russian);
-
V. A. Marčenko [Marchenko] and I. V. Ostrovskii, "A characterization of the spectrum of Hill's operator", Mat. Sb. (N.S.) 97 (139):4(8) (1975), 540-606 (Russian);
-
-
-
-
19
-
-
84980167496
-
Hill's operator and hyperelliptic function theory in the presence of infinitely many branch points
-
H. P. McKean and E. Trubowitz, "Hill's operator and hyperelliptic function theory in the presence of infinitely many branch points", Comm. Pure Appl. Math. 29:2 (1976), 143-226.
-
(1976)
Comm. Pure Appl. Math
, vol.29
, Issue.2
, pp. 143-226
-
-
McKean, H.P.1
Trubowitz, E.2
-
20
-
-
0345531328
-
The inverse problem of scattering theory for periodic finite-zone potentials
-
1 (1975, 65-66 Russian
-
B. A. Dubrovin, "The inverse problem of scattering theory for periodic finite-zone potentials", Funkcional. Anal. i Priložen. 9:1 (1975), 65-66 (Russian);
-
Funkcional. Anal. i Priložen
, vol.9
-
-
Dubrovin, B.A.1
-
22
-
-
84980187488
-
The inverse problem for periodic potentials
-
E. Trubowitz, "The inverse problem for periodic potentials", Comm. Pure Appl. Math. 30:3 (1977), 321-337.
-
(1977)
Comm. Pure Appl. Math
, vol.30
, Issue.3
, pp. 321-337
-
-
Trubowitz, E.1
-
23
-
-
0010068250
-
Gap estimates of the spectrum of the Zakharov-Shabat system
-
B. Grébert, T. Kappeler, and B. Mityagin, "Gap estimates of the spectrum of the Zakharov-Shabat system", Appl. Math. Lett. 11:4 (1998), 95-97.
-
(1998)
Appl. Math. Lett
, vol.11
, Issue.4
, pp. 95-97
-
-
Grébert, B.1
Kappeler, T.2
Mityagin, B.3
-
24
-
-
85164640366
-
-
B. Grébert and T. Kappeler, Estimates on periodic and Dirichlet eigenvalues for the Zakharov-Shabat system, Asymptot. Anal. 25:3-4 (2001), 201-237; Erratum, Asymptot. Anal. 29:2 (2002), 183.
-
B. Grébert and T. Kappeler, "Estimates on periodic and Dirichlet eigenvalues for the Zakharov-Shabat system", Asymptot. Anal. 25:3-4 (2001), 201-237; "Erratum", Asymptot. Anal. 29:2 (2002), 183.
-
-
-
-
25
-
-
0742333376
-
Spectra of 1-D periodic Dirac operators and smoothness of potentials
-
P. Djakov and B. Mityagin, "Spectra of 1-D periodic Dirac operators and smoothness of potentials", C. R. Math. Acad. Sci. Soc. R. Can. 25:4 (2003), 121-125.
-
(2003)
C. R. Math. Acad. Sci. Soc. R. Can
, vol.25
, Issue.4
, pp. 121-125
-
-
Djakov, P.1
Mityagin, B.2
-
26
-
-
23944472670
-
Instability zones of a periodic 1D Dirac operator and smoothness of its potential
-
P. Djakov and B. Mityagin, "Instability zones of a periodic 1D Dirac operator and smoothness of its potential", Comm. Math. Phys. 259:1 (2005), 139-183.
-
(2005)
Comm. Math. Phys
, vol.259
, Issue.1
, pp. 139-183
-
-
Djakov, P.1
Mityagin, B.2
-
30
-
-
0002260691
-
Spectral theory of ordinary differential operators
-
Springer-Verlag, Berlin
-
J. Weidmann, Spectral theory of ordinary differential operators, Lecture Notes in Math., vol. 1258, Springer-Verlag, Berlin 1987.
-
(1987)
Lecture Notes in Math
, vol.1258
-
-
Weidmann, J.1
-
31
-
-
84960605212
-
A linear differential equation with periodic coefficients
-
E. L. Ince, "A linear differential equation with periodic coefficients", Proc. London Math. Soc. (2) 23 (1924), 56-74.
-
(1924)
Proc. London Math. Soc. (2)
, vol.23
, pp. 56-74
-
-
Ince, E.L.1
-
32
-
-
0005424922
-
On the effect of the boundary conditions on the eigenvalues of ordinary differential equations
-
Baltimore, MD, Johns Hopkins Univ. Press, Baltimore, MD
-
E. M. Harrell II, "On the effect of the boundary conditions on the eigenvalues of ordinary differential equations", Contributions to analysis and geometry (Baltimore, MD, 1980), Johns Hopkins Univ. Press, Baltimore, MD 1981, pp. 139-150.
-
(1980)
Contributions to analysis and geometry
, pp. 139-150
-
-
Harrell II, E.M.1
-
33
-
-
0003153458
-
The asymptotics of the gap in the Mathieu equation
-
J. Avron and B. Simon, "The asymptotics of the gap in the Mathieu equation", Ann. Physics 134:1 (1981), 76-84.
-
(1981)
Ann. Physics
, vol.134
, Issue.1
, pp. 76-84
-
-
Avron, J.1
Simon, B.2
-
34
-
-
33846311286
-
Sur une série dans la théorie des équations différentielles linéaires du second ordre à coefficients périodiques, Pétersb. Mém.
-
A. Liapounoff, "Sur une série dans la théorie des équations différentielles linéaires du second ordre à coefficients périodiques", Pétersb. Mém. (8) Zap. Imp. Akad. Nauk, Fiz.-Mat. Otd. 13:2 (1903).
-
(1903)
Zap. Imp. Akad. Nauk, Fiz.-Mat. Otd
, vol.13
, pp. 2
-
-
Liapounoff, A.1
-
35
-
-
4444312601
-
Asymptotics of instability zones of Hill operators with a two term potential
-
P. Djakov and B. Mityagin, "Asymptotics of instability zones of Hill operators with a two term potential", C. R. Math. Acad. Sci. Paris 339:5 (2004), 351-354.
-
(2004)
C. R. Math. Acad. Sci. Paris
, vol.339
, Issue.5
, pp. 351-354
-
-
Djakov, P.1
Mityagin, B.2
-
36
-
-
85164631992
-
Asymptotics of instability zones of the Hill operator with a two term potential
-
to appear, arXiv: math-ph/0509034
-
P. Djakov and B. Mityagin, "Asymptotics of instability zones of the Hill operator with a two term potential", J. Funct. Anal. (to appear); arXiv: math-ph/0509034 (2005).
-
(2005)
J. Funct. Anal
-
-
Djakov, P.1
Mityagin, B.2
-
37
-
-
34250245130
-
Spectral analysis of a class of second-order non-self-adjoint differential operators
-
14-19 Russian
-
M. G. Gasymov, "Spectral analysis of a class of second-order non-self-adjoint differential operators", Funkcional. Anal. i Priložen. 14:1 (1980), 14-19 (Russian);
-
(1980)
Funkcional. Anal. i Priložen
, vol.14
, pp. 1
-
-
Gasymov, M.G.1
-
39
-
-
0039704276
-
Spectral analysis of a nonselfadjoint Hill operator
-
2 (1992, 248-252 Russian
-
V. A. Tkachenko, "Spectral analysis of a nonselfadjoint Hill operator", Dokl. Akad. Nauk SSSR 322:2 (1992), 248-252 (Russian);
-
Dokl. Akad. Nauk SSSR
, vol.322
-
-
Tkachenko, V.A.1
-
41
-
-
0030102735
-
Spectral parametrization of non-selfadjoint Hill's operators
-
J.-J. Sansuc and V. Tkachenko, "Spectral parametrization of non-selfadjoint Hill's operators", J. Differential Equations 125:2 (1996), 366-384.
-
(1996)
J. Differential Equations
, vol.125
, Issue.2
, pp. 366-384
-
-
Sansuc, J.-J.1
Tkachenko, V.2
-
42
-
-
0040154288
-
Discriminants and generic spectra of nonselfadjoint Hill's operators, Spectral operator theory and related topics, Adv. Soviet Math., vol. 19
-
V. Tkachenko, "Discriminants and generic spectra of nonselfadjoint Hill's operators", Spectral operator theory and related topics, Adv. Soviet Math., vol. 19, Amer. Math. Soc., Providence, RI 1994, pp. 41-71.
-
Amer. Math. Soc., Providence
, vol.RI 1994
, pp. 41-71
-
-
Tkachenko, V.1
-
43
-
-
0003806437
-
-
Naukova Dumka, Kiev, Russian, English transl, Oper. Theory Adv. Appl, Birkhäuser Verlag, Basel
-
V. A. Marchenko, Sturm-Liouville operators and applications, Naukova Dumka, Kiev 1977 (Russian); English transl., Oper. Theory Adv. Appl., vol. 22, Birkhäuser Verlag, Basel 1986.
-
(1977)
Sturm-Liouville operators and applications
, vol.22
-
-
Marchenko, V.A.1
-
44
-
-
85164632433
-
-
J.-J. Sansuc and V. Tkachenko, Spectral properties of non-selfadjoint Hill's operators with smooth potentials, Algebraic and geometric methods in mathematical physics (Kaciveli, 1993) (A. Boutet de Monvel and V. Marčenko, eds.), Math. Phys. Stud., 19, Kluwer Acad. Publ., Dordrecht 1996, pp. 371-385.
-
J.-J. Sansuc and V. Tkachenko, "Spectral properties of non-selfadjoint Hill's operators with smooth potentials", Algebraic and geometric methods in mathematical physics (Kaciveli, 1993) (A. Boutet de Monvel and V. Marčenko, eds.), Math. Phys. Stud., vol. 19, Kluwer Acad. Publ., Dordrecht 1996, pp. 371-385.
-
-
-
-
45
-
-
22444456226
-
Gap estimates of the spectrum of Hill's equation and action variables for KdV
-
T. Kappeler and B. Mityagin, "Gap estimates of the spectrum of Hill's equation and action variables for KdV", Trans. Amer. Math. Soc. 351:2 (1999), 619-646.
-
(1999)
Trans. Amer. Math. Soc
, vol.351
, Issue.2
, pp. 619-646
-
-
Kappeler, T.1
Mityagin, B.2
-
46
-
-
0035527618
-
Estimates for periodic and Dirichlet eigenvalues of the Schrödinger operator
-
T. Kappeler and B. Mityagin, "Estimates for periodic and Dirichlet eigenvalues of the Schrödinger operator", SIAM J. Math. Anal 33:1 (2001), 113-152.
-
(2001)
SIAM J. Math. Anal
, vol.33
, Issue.1
, pp. 113-152
-
-
Kappeler, T.1
Mityagin, B.2
-
47
-
-
0037145461
-
Smoothness of Schrödinger operator potential in the case of Gevrey type asymptotics of the gaps
-
P. Djakov and B. Mityagin, "Smoothness of Schrödinger operator potential in the case of Gevrey type asymptotics of the gaps", J. Funct. Anal. 195:1 (2002), 89-128.
-
(2002)
J. Funct. Anal
, vol.195
, Issue.1
, pp. 89-128
-
-
Djakov, P.1
Mityagin, B.2
-
48
-
-
4444381849
-
Spectral triangles of Schrödinger operators with complex potentials
-
P. Djakov and B. Mityagin, "Spectral triangles of Schrödinger operators with complex potentials", Selecta Math. (N.S.) 9:4 (2003), 495-528.
-
(2003)
Selecta Math. (N.S.)
, vol.9
, Issue.4
, pp. 495-528
-
-
Djakov, P.1
Mityagin, B.2
-
49
-
-
0003862232
-
-
corr. 2nd ed, Math. Wissenschaften, Springer-Verlag, Berlin, Reprint, Classics in Math, Springer-Verlag, Berlin
-
T. Kato, Perturbation theory for linear operators, corr. 2nd ed., Grund. Math. Wissenschaften, vol. 132, Springer-Verlag, Berlin 1980; Reprint, Classics in Math., Springer-Verlag, Berlin 1995.
-
(1980)
Perturbation theory for linear operators
, vol.132
-
-
Kato, T.1
-
50
-
-
0003687441
-
Methods of modern mathematical physics
-
Academic Press, New York-London
-
M. Reed and B. Simon, Methods of modern mathematical physics. II: Fourier analysis, self-adjointness, Academic Press, New York-London 1975.
-
(1975)
II: Fourier analysis, self-adjointness
-
-
Reed, M.1
Simon, B.2
-
52
-
-
85164648019
-
-
English transl., Transl. Math. Monographs, 39, Amer. Math. Soc., Providence, RI 1975.
-
English transl., Transl. Math. Monographs, vol. 39, Amer. Math. Soc., Providence, RI 1975.
-
-
-
-
53
-
-
85164645783
-
-
I. M. Gel'fand, Expansion in characteristic functions of an equation with periodic coefficients, Dokl. Akad. Nauk SSSR (N.S.) 73:6 (1950), 1117-1120. (Russian)
-
I. M. Gel'fand, "Expansion in characteristic functions of an equation with periodic coefficients", Dokl. Akad. Nauk SSSR (N.S.) 73:6 (1950), 1117-1120. (Russian)
-
-
-
-
54
-
-
0040296215
-
On the spectrum of non-selfadjoint differential operators with periodic coefficients
-
6 (1963, 1312-1315 Russian
-
F. S. Rofe-Beketov, "On the spectrum of non-selfadjoint differential operators with periodic coefficients", Dokl. Akad. Nauk SSSR 152:6 (1963), 1312-1315 (Russian);
-
Dokl. Akad. Nauk SSSR
, vol.152
-
-
Rofe-Beketov, F.S.1
-
56
-
-
3042832886
-
Spectral analysis of differential operators. Interplay between spectral and oscillatory properties
-
World Scientific, Hackensack, NJ
-
F. S. Rofe-Beketov and A. M. Kholkin, Spectral analysis of differential operators. Interplay between spectral and oscillatory properties, World Scientific Monograph Series in Mathematics, vol. 7, World Scientific, Hackensack, NJ 2005.
-
(2005)
World Scientific Monograph Series in Mathematics
, vol.7
-
-
Rofe-Beketov, F.S.1
Kholkin, A.M.2
-
57
-
-
5644304461
-
Convergence of expansions in eigenfunctions of the Dirac operator
-
4 (2003, 456-459 Russian
-
B. S. Mityagin, "Convergence of expansions in eigenfunctions of the Dirac operator", Dokl. Akad. Nauk 393:4 (2003), 456-459 (Russian);
-
Dokl. Akad. Nauk
, vol.393
-
-
Mityagin, B.S.1
-
59
-
-
12344330160
-
Spectral expansions of one-dimensional periodic Dirac operators
-
B. Mityagin, "Spectral expansions of one-dimensional periodic Dirac operators", Dyn. Partial Differ. Equ. 1:2 (2004), 125-191.
-
(2004)
Dyn. Partial Differ. Equ
, vol.1
, Issue.2
, pp. 125-191
-
-
Mityagin, B.1
-
60
-
-
22944464221
-
Schrödinger operators with singular potentials from spaces of multipliers
-
5 (1999, 723-733 Russian
-
M. I. Neiman-zade and A. A. Shkalikov, "Schrödinger operators with singular potentials from spaces of multipliers", Mat. Zametki 66:5 (1999), 723-733 (Russian);
-
Mat. Zametki
, vol.66
-
-
Neiman-zade, M.I.1
Shkalikov, A.A.2
-
61
-
-
85164638475
-
-
English transl., Math. Notes 66:5-6 (1999), 599-607.
-
(1999)
Math. Notes
, vol.66
, Issue.5-6
, pp. 599-607
-
-
English transl1
-
62
-
-
3042830532
-
Sturm-Liouville operators with distribution potentials
-
Russian
-
A. M. Savchuk and A. A. Shkalikov, "Sturm-Liouville operators with distribution potentials", Tr. Mosk. Mat. Obs. 64 (2003), 159-212 (Russian);
-
(2003)
Tr. Mosk. Mat. Obs
, vol.64
, pp. 159-212
-
-
Savchuk, A.M.1
Shkalikov, A.A.2
-
64
-
-
0003568896
-
-
Nauka, Moscow, Russian
-
M. A. Krasnosel'skii, G. M. Vainikko, P. P. Zabreiko, Ya. B. Rutitskii, and V.Ya. Stetsenko, Approximate solution of operator equations, Nauka, Moscow 1969 (Russian);
-
(1969)
Approximate solution of operator equations
-
-
Krasnosel'skii, M.A.1
Vainikko, G.M.2
Zabreiko, P.P.3
Rutitskii, Y.B.4
Stetsenko, V.Y.5
-
66
-
-
0030539342
-
One-dimensional periodic Dirac Hamiltonians: Semiclassical and high-energy asymptotics for gaps
-
G. Nenciu and R. Purice, "One-dimensional periodic Dirac Hamiltonians: semiclassical and high-energy asymptotics for gaps", J. Math. Phys. 37:7 (1996), 3153-3167.
-
(1996)
J. Math. Phys
, vol.37
, Issue.7
, pp. 3153-3167
-
-
Nenciu, G.1
Purice, R.2
-
67
-
-
0003938791
-
-
Grund. Math. Wissenschaften, Springer-Verlag, Berlin
-
G. Pólya and G. Szegö, Problems and theorems in analysis. I: Series, integral calculus, theory of functions, Grund. Math. Wissenschaften, vol. 193, Springer-Verlag, Berlin 1978;
-
(1978)
Problems and theorems in analysis. I: Series, integral calculus, theory of functions
, vol.193
-
-
Pólya, G.1
Szegö, G.2
-
68
-
-
85164632973
-
-
Reprint, Classics in Math., Springer-Verlag, Berlin 1998.
-
Reprint, Classics in Math., Springer-Verlag, Berlin 1998.
-
-
-
-
70
-
-
85164643067
-
-
I. M. Gel'fand and G. E. Shilov, Generalized functions, 2: Spaces of fundamental and generalized functions, Fizmatlit, Moscow 1958 (Russian); English transl., Academic Press, New York 1968; reprint, Harcourt-Brace, New York-London 1977.
-
I. M. Gel'fand and G. E. Shilov, Generalized functions, vol. 2: Spaces of fundamental and generalized functions, Fizmatlit, Moscow 1958 (Russian); English transl., Academic Press, New York 1968; reprint, Harcourt-Brace, New York-London 1977.
-
-
-
-
71
-
-
85164656998
-
-
Universität Stuttgart, Stuttgart
-
J. Pöschel, Hill's potentials in weighted Sobolev spaces and their spectral gaps, Preprint, Institut für Analysis, Dynamik und Optimierung, Universität Stuttgart, Stuttgart 2004; http://www.poschel.de/ pbl/w-gaps.pdf.
-
(2004)
Hill's potentials in weighted Sobolev spaces and their spectral gaps, Preprint, Institut für Analysis, Dynamik und Optimierung
-
-
Pöschel, J.1
-
72
-
-
0039895724
-
Characterization of Hill operators with analytic potentials
-
V. Tkachenko, "Characterization of Hill operators with analytic potentials", Integral Equations Operator Theory 41:3 (2001), 360-380.
-
(2001)
Integral Equations Operator Theory
, vol.41
, Issue.3
, pp. 360-380
-
-
Tkachenko, V.1
-
73
-
-
0040078556
-
On the absolute convergence of expansions in eigenfunctions of certain differential operators
-
Russian
-
G. M. Kesel'man, "On the absolute convergence of expansions in eigenfunctions of certain differential operators", Izv. Vysš. Učebn. Zaved. Matematika 1984:2(39), 82-93. (Russian)
-
(1984)
Izv. Vysš. Učebn. Zaved. Matematika
, vol.2
, Issue.39
, pp. 82-93
-
-
Kesel'man, G.M.1
-
74
-
-
85164649984
-
-
2(0,1), Dokl. Akad. Nauk SSSR 144:5 (1962), 981-984 (Russian);
-
2(0,1)", Dokl. Akad. Nauk SSSR 144:5 (1962), 981-984 (Russian);
-
-
-
-
76
-
-
13644250428
-
An eigenvalue problem for a nonlinear Sturm-Liouville equation with boundary conditions depending on the spectral parameter
-
2 (2004, 161-164 Russian
-
A. S. Makin, "An eigenvalue problem for a nonlinear Sturm-Liouville equation with boundary conditions depending on the spectral parameter", Dokl Akad. Nauk 399:2 (2004), 161-164 (Russian);
-
Dokl Akad. Nauk
, vol.399
-
-
Makin, A.S.1
-
78
-
-
85153160409
-
-
Frederick Ungar Publ. Co, New York
-
M. A. Naimark, Linear differential operators, Part I: Elementary theory of linear differential operators, Frederick Ungar Publ. Co., New York 1967; Part II: Linear differential operators in Hilbert space, Frederick Ungar Publ. Co., New York 1968.
-
(1968)
Linear differential operators, Part I: Elementary theory of linear differential operators, Frederick Ungar Publ. Co., New York 1967; Part II: Linear differential operators in Hilbert space
-
-
Naimark, M.A.1
-
79
-
-
0348119318
-
A proof of the impossibility of the coexistence of two Mathieu functions
-
E. L. Ince, "A proof of the impossibility of the coexistence of two Mathieu functions", Proc. Cambridge Philos. Soc. 21 (1922), 117-120.
-
(1922)
Proc. Cambridge Philos. Soc
, vol.21
, pp. 117-120
-
-
Ince, E.L.1
-
80
-
-
84960572218
-
On the zeros of Mathieu functions
-
E. Hille, "On the zeros of Mathieu functions", Proc. London Math. Soc. (2) 23 (1924), 185-237.
-
(1924)
Proc. London Math. Soc. (2)
, vol.23
, pp. 185-237
-
-
Hille, E.1
-
81
-
-
20944442440
-
On the impossibility of simultaneous existence of two Mathieu functions
-
Z. Markovic, "On the impossibility of simultaneous existence of two Mathieu functions", Proc. Cambridge Philos. Soc. 23 (1926), 203-205.
-
(1926)
Proc. Cambridge Philos. Soc
, vol.23
, pp. 203-205
-
-
Markovic, Z.1
-
82
-
-
0004119596
-
-
Clarendon Press, Oxford, corr. reprint, Dover Publ, New York
-
N. W. McLachlan, Theory and applications of Mathieu functions, Clarendon Press, Oxford 1947; corr. reprint, Dover Publ., New York 1964.
-
(1947)
Theory and applications of Mathieu functions
-
-
McLachlan, N.W.1
-
83
-
-
20944443203
-
The coexistence problem for Hill's equation
-
no. BR-26, New York University, Institute of Mathematical Sciences, Division of Electromagnetic Research, New York
-
S. Winkler and W. Magnus, The coexistence problem for Hill's equation, Research Report no. BR-26, New York University, Institute of Mathematical Sciences, Division of Electromagnetic Research, New York 1958.
-
(1958)
Research Report
-
-
Winkler, S.1
Magnus, W.2
-
84
-
-
84980087992
-
Instability intervals of Hill's equation
-
D. M. Levy and J. B. Keller, "Instability intervals of Hill's equation", Comm. Pure Appl. Math. 16 (1963), 469-476.
-
(1963)
Comm. Pure Appl. Math
, vol.16
, pp. 469-476
-
-
Levy, D.M.1
Keller, J.B.2
-
85
-
-
4043048841
-
The asymptotics of spectral gaps of a 1D Dirac operator with cosine potential
-
P. Djakov and B. Mityagin, "The asymptotics of spectral gaps of a 1D Dirac operator with cosine potential", Lett. Math. Phys. 65:2 (2003), 95-108.
-
(2003)
Lett. Math. Phys
, vol.65
, Issue.2
, pp. 95-108
-
-
Djakov, P.1
Mityagin, B.2
-
86
-
-
12344332690
-
Multiplicities of the eigenvalues of periodic Dirac operators
-
P. Djakov and B. Mityagin, "Multiplicities of the eigenvalues of periodic Dirac operators", J. Differential Equations 210:1 (2005), 178-216.
-
(2005)
J. Differential Equations
, vol.210
, Issue.1
, pp. 178-216
-
-
Djakov, P.1
Mityagin, B.2
-
87
-
-
0000466619
-
Estimations asymptotiques des intervalles d'instabilité pour l'équation de Hill
-
A. Grigis, "Estimations asymptotiques des intervalles d'instabilité pour l'équation de Hill", Ann. Sci. École Norm. Sup. (4) 20:4 (1987), 641-672.
-
(1987)
Ann. Sci. École Norm. Sup. (4)
, vol.20
, Issue.4
, pp. 641-672
-
-
Grigis, A.1
-
88
-
-
84958734984
-
On a class of differential equations whose solutions satisfy integral equations
-
E. T. Whittaker, "On a class of differential equations whose solutions satisfy integral equations", Proc. Edinburgh Math. Soc. 33 (1914-1915), 14-23.
-
(1914)
Proc. Edinburgh Math. Soc
, vol.33
, pp. 14-23
-
-
Whittaker, E.T.1
-
89
-
-
20944441301
-
Simple and double eigenvalues of the Hill operator with a two-term potential
-
P. Djakov and B. Mityagin, "Simple and double eigenvalues of the Hill operator with a two-term potential", J. Approx. Theory 135:1 (2005), 70-104.
-
(2005)
J. Approx. Theory
, vol.135
, Issue.1
, pp. 70-104
-
-
Djakov, P.1
Mityagin, B.2
-
90
-
-
85164656738
-
-
A. V. Turbiner, Quantum mechanics: problems intermediate between exactly solvable and completely unsolvable, Zh. Èksper. Teoret. Fiz. 94:2 (1988), 33-44 (Russian);
-
A. V. Turbiner, "Quantum mechanics: problems intermediate between exactly solvable and completely unsolvable", Zh. Èksper. Teoret. Fiz. 94:2 (1988), 33-44 (Russian);
-
-
-
-
92
-
-
0009491906
-
Quasi-exactly-solvable problems and sl(2) algebra
-
A. V. Turbiner, "Quasi-exactly-solvable problems and sl(2) algebra", Comm. Math. Phys. 118:3 (1988), 467-474.
-
(1988)
Comm. Math. Phys
, vol.118
, Issue.3
, pp. 467-474
-
-
Turbiner, A.V.1
-
93
-
-
33846294645
-
Instability intervals of the Ince and Hill equations
-
H. Volkmer, "Instability intervals of the Ince and Hill equations", Analysis 25 (2005), 189-204.
-
(2005)
Analysis
, vol.25
, pp. 189-204
-
-
Volkmer, H.1
-
94
-
-
0038970127
-
On the spectral theory of Schrödinger operators with periodic complex-valued potentials
-
2 (1988, 85-86 Russian
-
L. A. Pastur and V. A. Tkachenko, "On the spectral theory of Schrödinger operators with periodic complex-valued potentials", Funktsional. Anal. i Prilozhen. 22:2 (1988), 85-86 (Russian);
-
Funktsional. Anal. i Prilozhen
, vol.22
-
-
Pastur, L.A.1
Tkachenko, V.A.2
-
96
-
-
85164648760
-
Inverse problem for the Sturm-Liouville operator with almost-periodic potential having only positive Fourier exponents, Entire and subharmonic functions, Adv. Soviet Math., vol. 11
-
M. Simbirskii, "Inverse problem for the Sturm-Liouville operator with almost-periodic potential having only positive Fourier exponents", Entire and subharmonic functions, Adv. Soviet Math., vol. 11, Amer. Math. Soc., Providence, RI 1992, pp. 21-38.
-
Amer. Math. Soc., Providence
, vol.RI 1992
, pp. 21-38
-
-
Simbirskii, M.1
-
97
-
-
0347622498
-
On half-line spectra for a class of non-self-adjoint Hill operators
-
K. C. Shin, "On half-line spectra for a class of non-self-adjoint Hill operators", Math. Nachr. 261/262 (2003), 171-175.
-
(2003)
Math. Nachr
, vol.261-262
, pp. 171-175
-
-
Shin, K.C.1
-
98
-
-
33645871285
-
Trace formula and spectral Riemann surfaces for a class of tri-diagonal matrices
-
P. Djakov and B. Mityagin, "Trace formula and spectral Riemann surfaces for a class of tri-diagonal matrices", J. Approx. Theory 139:1-2 (2006), 293-326.
-
(2006)
J. Approx. Theory
, vol.139
, Issue.1-2
, pp. 293-326
-
-
Djakov, P.1
Mityagin, B.2
-
99
-
-
0142246421
-
Spectral gaps of the periodic Schrödinger operator when its potential is an entire function
-
P. Djakov and B. Mityagin, "Spectral gaps of the periodic Schrödinger operator when its potential is an entire function", Adv. in Appl. Math. 31:3 (2003), 562-596.
-
(2003)
Adv. in Appl. Math
, vol.31
, Issue.3
, pp. 562-596
-
-
Djakov, P.1
Mityagin, B.2
-
100
-
-
0041197846
-
Approximation of periodic by finite-zone potentials
-
Russian
-
V. A. Marchenko and I. V. Ostrovskii, "Approximation of periodic by finite-zone potentials", Vestnik Khar'kov. Gos. Univ., 1980, no. 205, 4-40 (Russian);
-
(1980)
Vestnik Khar'kov. Gos. Univ
, Issue.205
, pp. 4-40
-
-
Marchenko, V.A.1
Ostrovskii, I.V.2
-
101
-
-
85164643042
-
-
English transl., Selecta Math. Soviet. 6:2 (1987), 101-136; Corrections to the article, Selecta Math. Soviet. 7:1 (1988), 99-100.
-
English transl., Selecta Math. Soviet. 6:2 (1987), 101-136; Corrections to the article, Selecta Math. Soviet. 7:1 (1988), 99-100.
-
-
-
-
102
-
-
0010118175
-
Characterization of the spectra of the periodic and antiperiodic boundary value problems that are generated by the Dirac operator
-
Vishcha Shkola, Khar'kov
-
T. V. Misyura, "Characterization of the spectra of the periodic and antiperiodic boundary value problems that are generated by the Dirac operator", Teor. Funktsii Funktsional. Anal. i Prilozhen., no. 30, Vishcha Shkola, Khar'kov 1978, pp. 90-101;
-
(1978)
Teor. Funktsii Funktsional. Anal. i Prilozhen
, Issue.30
, pp. 90-101
-
-
Misyura, T.V.1
-
103
-
-
0000894032
-
Characterization of the spectra of the periodic and antiperiodic boundary value problems that are generated by the Dirac operator. II
-
Vishcha Shkola, Khar'kov, Russian
-
"Characterization of the spectra of the periodic and antiperiodic boundary value problems that are generated by the Dirac operator. II", Teor. Funktsii Funktsional Anal. i Prilozhen., no. 31, Vishcha Shkola, Khar'kov 1979, pp. 102-109. (Russian)
-
(1979)
Teor. Funktsii Funktsional Anal. i Prilozhen
, Issue.31
, pp. 102-109
-
-
-
104
-
-
0040794268
-
Non-selfadjoint periodic Dirac operators with finite-band spectra
-
V. Tkachenko, "Non-selfadjoint periodic Dirac operators with finite-band spectra", Integral Equations Operator Theory 36:3 (2000), 325-348.
-
(2000)
Integral Equations Operator Theory
, vol.36
, Issue.3
, pp. 325-348
-
-
Tkachenko, V.1
-
105
-
-
0142198231
-
Non-selfadjoint periodic Dirac operators
-
Beer-Sheva/Rehovot, Oper. Theory Adv. Appl, Birkhäuser Verlag, Basel
-
V. Tkachenko, "Non-selfadjoint periodic Dirac operators", Operator theory, system theory and related topics (Beer-Sheva/Rehovot, 1997), Oper. Theory Adv. Appl., vol. 123, Birkhäuser Verlag, Basel 2001, pp. 485-512.
-
(1997)
Operator theory, system theory and related topics
, vol.123
, pp. 485-512
-
-
Tkachenko, V.1
-
106
-
-
84887256905
-
Density of finite gap potentials for the Zakharov-Shabat system
-
B. Grébert and T. Kappeler, "Density of finite gap potentials for the Zakharov-Shabat system", Asymptot. Anal. 33:1 (2003), 1-8.
-
(2003)
Asymptot. Anal
, vol.33
, Issue.1
, pp. 1-8
-
-
Grébert, B.1
Kappeler, T.2
|