메뉴 건너뛰기




Volumn , Issue 22, 2004, Pages 1087-1097

Necessary and Sufficient Conditions in the Spectral Theory of Jacobi Matrices and Schrödinger Operators

Author keywords

[No Author keywords available]

Indexed keywords


EID: 2142795885     PISSN: 10737928     EISSN: None     Source Type: Journal    
DOI: 10.1155/s1073792804132790     Document Type: Article
Times cited : (13)

References (42)
  • 1
    • 84968476182 scopus 로고
    • A convergence equivalence related to polynomials orthogonal on the unit circle
    • G. Baxter, A convergence equivalence related to polynomials orthogonal on the unit circle, Trans. Amer. Math. Soc. 99 (1961), 471-487.
    • (1961) Trans. Amer. Math. Soc. , vol.99 , pp. 471-487
    • Baxter, G.1
  • 2
    • 84953818707 scopus 로고
    • A norm inequality for a "finite-section" Wiener-Hopf equation
    • _, A norm inequality for a "finite-section" Wiener-Hopf equation, Illinois J. Math. 7 (1963), 97-103.
    • (1963) Illinois J. Math. , vol.7 , pp. 97-103
  • 3
    • 0004000819 scopus 로고
    • Inverse Problems in Quantum Scattering Theory, 2nd ed.
    • Springer-Verlag, New York
    • K. Chadan and P. C. Sabatier, Inverse Problems in Quantum Scattering Theory, 2nd ed., Texts and Monographs in Physics, Springer-Verlag, New York, 1989.
    • (1989) Texts and Monographs in Physics
    • Chadan, K.1    Sabatier, P.C.2
  • 6
    • 0007035802 scopus 로고    scopus 로고
    • On the absolutely continuous spectrum of one-dimensional Schrödinger operators with square summable potentials
    • P. Deift and R. Killip, On the absolutely continuous spectrum of one-dimensional Schrödinger operators with square summable potentials, Comm. Math. Phys. 203 (1999), no. 2, 341-347.
    • (1999) Comm. Math. Phys. , vol.203 , Issue.2 , pp. 341-347
    • Deift, P.1    Killip, R.2
  • 7
    • 0038626232 scopus 로고    scopus 로고
    • On the coexistence of absolutely continuous and singular continuous components of the spectral measure for some Sturm-Liouville operators with square summable potential
    • S. A. Denisov, On the coexistence of absolutely continuous and singular continuous components of the spectral measure for some Sturm-Liouville operators with square summable potential, J. Differential Equations 191 (2003), no. 1, 90-104.
    • (2003) J. Differential Equations , vol.191 , Issue.1 , pp. 90-104
    • Denisov, S.A.1
  • 8
    • 0003446044 scopus 로고    scopus 로고
    • Dover Publications,New York
    • p Spaces, Dover Publications, New York, 2000.
    • (2000) p Spaces
    • Duren, P.L.1
  • 9
    • 0003709960 scopus 로고
    • The Asymptotic Solution of Linear Differential Systems. Applications of the Levinson Theorem
    • The Clarendon Press, Oxford University Press, New York
    • M. S. P. Eastham, The Asymptotic Solution of Linear Differential Systems. Applications of the Levinson Theorem, London Mathematical Society Monographs. New Series, vol. 4, The Clarendon Press, Oxford University Press, New York, 1989.
    • (1989) London Mathematical Society Monographs. New Series , vol.4
    • Eastham, M.S.P.1
  • 10
    • 84980193643 scopus 로고
    • Korteweg-deVries equation and generalization. VI. Methods for exact solution
    • C. S. Gardner, J. M. Greene, M. D. Kruskal, and R. M. Miura, Korteweg-deVries equation and generalization. VI. Methods 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
  • 11
    • 0001458591 scopus 로고
    • On the determination of a differential equation from its spectral function
    • Russian
    • I. M. Gel'fand and B. M. Levitan, On the determination of a differential equation from its spectral function, Izv. Akad. Nauk SSSR Ser. Mat. 15 (1951), 309-360 (Russian).
    • (1951) Izv. Akad. Nauk SSSR Ser. Mat. , vol.15 , pp. 309-360
    • Gel'Fand, I.M.1    Levitan, B.M.2
  • 12
    • 0001649889 scopus 로고
    • On the determination of a differential equation from its spectral function
    • _, On the determination of a differential equation from its spectral function, Amer. Math. Soc. Transl. Ser. 2 1 (1955), 253-304.
    • (1955) Amer. Math. Soc. Transl. Ser. 2 , vol.1 , pp. 253-304
  • 13
    • 21344496328 scopus 로고
    • Scattering theory, orthogonal polynomials, and q-series
    • J. S. Geronimo, Scattering theory, orthogonal polynomials, and q-series, SIAM J. Math. Anal. 25 (1994), no. 2, 392-419.
    • (1994) SIAM J. Math. Anal. , vol.25 , Issue.2 , pp. 392-419
    • Geronimo, J.S.1
  • 14
    • 0034257480 scopus 로고    scopus 로고
    • A new approach to inverse spectral theory. II. General real potentials and the connection to the spectral measure
    • F. Gesztesy and B. Simon, A new approach to inverse spectral theory. II. General real potentials and the connection to the spectral measure, Ann. of Math. (2) 152 (2000), no. 2, 593-643.
    • (2000) Ann. of Math.(2) , vol.152 , Issue.2 , pp. 593-643
    • Gesztesy, F.1    Simon, B.2
  • 16
    • 84956112010 scopus 로고
    • On convergence of Padé approximants for some classes of meromorphic functions
    • A. A. Gončar, On convergence of Padé approximants for some classes of meromorphic functions, Math. USSR-Sb. 26 (1975), 555-575.
    • (1975) Math. USSR-Sb. , vol.26 , pp. 555-575
    • Gončar, A.A.1
  • 17
    • 84968466719 scopus 로고
    • Unrestricted solution fields of almost-separable differential equations
    • P. Hartman, Unrestricted solution fields of almost-separable differential equations, Trans. Amer. Math. Soc. 63 (1948), 560-580.
    • (1948) Trans. Amer. Math. Soc. , vol.63 , pp. 560-580
    • Hartman, P.1
  • 18
    • 0002148022 scopus 로고
    • Asymptotic integrations of linear differential equations
    • erratum: Amer. J. Math. 77 (1955), 404
    • P. Hartman and A. Wintner, Asymptotic integrations of linear differential equations, Amer. J. Math. 77 (1955), 45-86; erratum: Amer. J. Math. 77 (1955), 404.
    • (1955) Amer. J. Math. , vol.77 , pp. 45-86
    • Hartman, P.1    Wintner, A.2
  • 19
    • 2142680042 scopus 로고
    • A theorem of Gabor Szego
    • Russian
    • I. A. Ibragimov, A theorem of Gabor Szego, Mat. Zametki 3 (1968), 693-702 (Russian).
    • (1968) Mat. Zametki , vol.3 , pp. 693-702
    • Ibragimov, I.A.1
  • 20
    • 0141614025 scopus 로고    scopus 로고
    • Sum rules for Jacobi matrices and their applications to spectral theory
    • R. Killip and B. Simon, Sum rules for Jacobi matrices and their applications to spectral theory, Ann. of Math. (2) 158 (2003), no. 1, 253-321.
    • (2003) Ann. of Math.(2) , vol.158 , Issue.1 , pp. 253-321
    • Killip, R.1    Simon, B.2
  • 21
    • 8744316165 scopus 로고    scopus 로고
    • in preparation
    • 2 potentials, in preparation.
    • 2 Potentials
  • 22
    • 0039793963 scopus 로고
    • Introduction to Spectral Theory: Selfadjoint Ordinary Differential Operators
    • American Mathematical Society, Rhode Island
    • B. M. Levitan and I. S. Sargsjan, Introduction to Spectral Theory: Selfadjoint Ordinary Differential Operators, Translations of Mathematical Monographs, vol. 39, American Mathematical Society, Rhode Island, 1975.
    • (1975) Translations of Mathematical Monographs , vol.39
    • Levitan, B.M.1    Sargsjan, I.S.2
  • 23
    • 0002624077 scopus 로고
    • Inequalities for the moments of the eigenvalues of the Schrödinger Hamiltonian and their relation to Sobolev inequalities
    • Princeton University Press, New Jersey
    • E. H. Lieb and W. Thirring, Inequalities for the moments of the eigenvalues of the Schrödinger Hamiltonian and their relation to Sobolev inequalities, Studies in Mathematical Physics. Essays in Honor of Valentine Bargmann, Princeton University Press, New Jersey, 1976, pp. 269303.
    • (1976) Studies in Mathematical Physics. Essays in Honor of Valentine Bargmann , pp. 269303
    • Lieb, E.H.1    Thirring, W.2
  • 24
    • 0000956929 scopus 로고
    • Orthogonal polynomials
    • P. Nevai, Orthogonal polynomials, Mem. Amer. Math. Soc. 18 (1979), no. 213, v+185.
    • (1979) Mem. Amer. Math. Soc. , vol.18 , Issue.213
    • Nevai, P.1
  • 25
    • 0001786022 scopus 로고
    • Orthogonal polynomials and their zeros
    • P. Nevai and V. Totik, Orthogonal polynomials and their zeros, Acta Sci. Math. (Szeged) 53 (1989), no. 1-2, 99-104.
    • (1989) Acta Sci. Math. (Szeged) , vol.53 , Issue.1-2 , pp. 99-104
    • Nevai, P.1    Totik, V.2
  • 26
    • 0000023186 scopus 로고
    • Discrete Sturm-Liouville operators and some problems of function theory
    • E. M. Nikishin, Discrete Sturm-Liouville operators and some problems of function theory, J. Soviet Math. 35 (1986), 2679-2744.
    • (1986) J. Soviet Math. , vol.35 , pp. 2679-2744
    • Nikishin, E.M.1
  • 27
    • 23044531005 scopus 로고    scopus 로고
    • Asymptotics of orthonormal polynomials in the presence of a denumerable set of mass points
    • F. Peherstorfer and P. Yuditskii, Asymptotics of orthonormal polynomials in the presence of a denumerable set of mass points, Proc. Amer. Math. Soc. 129 (2001), no. 11, 3213-3220.
    • (2001) Proc. Amer. Math. Soc. , vol.129 , Issue.11 , pp. 3213-3220
    • Peherstorfer, F.1    Yuditskii, P.2
  • 29
    • 0033235955 scopus 로고    scopus 로고
    • A new approach to inverse spectral theory. I. Fundamental formalism
    • B. Simon, A new approach to inverse spectral theory. I. Fundamental formalism, Ann. of Math. (2) 150 (1999), no. 3, 1029-1057.
    • (1999) Ann. of Math.(2) , vol.150 , Issue.3 , pp. 1029-1057
    • Simon, B.1
  • 30
    • 2142789965 scopus 로고    scopus 로고
    • A canonical factorization for meromorphic Herglotz functions on the unit disk sum rules for Jacobi matrices
    • to appear
    • _, A canonical factorization for meromorphic Herglotz functions on the unit disk and sum rules for Jacobi matrices, to appear in J. Funct. Anal.
    • J. Funct. Anal.
  • 31
    • 2142668891 scopus 로고    scopus 로고
    • Orthogonal Polynomials on the Unit Circle
    • American Mathematical Society, Rhode Island, in press
    • _, Orthogonal Polynomials on the Unit Circle, AMS Colloquium Publications Series, American Mathematical Society, Rhode Island, in press.
    • AMS Colloquium Publications Series
  • 32
    • 0344552002 scopus 로고    scopus 로고
    • Sum rules and the Szego condition for orthogonal polynomials on the real line
    • B. Simon and A. Zlatoš, Sum rules and the Szego condition for orthogonal polynomials on the real line, Comm. Math. Phys. 242 (2003) 393-423.
    • (2003) Comm. Math. Phys. , vol.242 , pp. 393-423
    • Simon, B.1    Zlatoš, A.2
  • 33
    • 0002593008 scopus 로고
    • Recherches sur les fractions continues
    • T. Stieltjes, Recherches sur les fractions continues, Ann. Fac. Sci. Univ. Toulouse, 8 (1894-1895), 1-122; 9, A5-A47.
    • (1894) Ann. Fac. Sci. Univ. Toulouse , vol.8 , pp. 1-122
    • Stieltjes, T.1
  • 34
    • 24444458493 scopus 로고    scopus 로고
    • T. Stieltjes, Recherches sur les fractions continues, Ann. Fac. Sci. Univ. Toulouse, 8 (1894-1895), 1-122; 9, A5-A47.
    • Ann. Fac. Sci. Univ. Toulouse , vol.9
  • 35
    • 0032201841 scopus 로고    scopus 로고
    • Linear and nonlinear inverse scattering
    • J. Sylvester and D. P. Winebrenner, Linear and nonlinear inverse scattering, SIAM J. Appl. Math. 59 (1999), no. 2, 669-699.
    • (1999) SIAM J. Appl. Math. , vol.59 , Issue.2 , pp. 669-699
    • Sylvester, J.1    Winebrenner, D.P.2
  • 36
    • 0000359705 scopus 로고
    • Ein Grenzwertsatz über die Toeplitzschen Determinanten einer reellen positiven Funktion
    • German
    • G. Szego, Ein Grenzwertsatz über die Toeplitzschen Determinanten einer reellen positiven Funktion, Math. Ann. 76 (1915), 490-503 (German).
    • (1915) Math. Ann. , vol.76 , pp. 490-503
    • Szego, G.1
  • 37
    • 34250944353 scopus 로고
    • Beiträge zur Theorie der Toeplitzschen Formen I
    • German
    • _, Beiträge zur Theorie der Toeplitzschen Formen, I, Math. Z. 6 (1920), 167-202 (German).
    • (1920) Math. Z. , vol.6 , pp. 167-202
  • 38
    • 0010627193 scopus 로고
    • Beiträge zur Theorie der Toeplitzschen Formen, II
    • German
    • _, Beiträge zur Theorie der Toeplitzschen Formen, II, Math. Z. 9 (1921), 167-190 (German).
    • (1921) Math. Z. , vol.9 , pp. 167-190
  • 39
    • 8744306351 scopus 로고
    • Über den asymptotischen Ausdruck von Polynomen, die durch eine Orthogonalitätseigenschaft definiert sind
    • German
    • _, Über den asymptotischen Ausdruck von Polynomen, die durch eine Orthogonalitätseigenschaft definiert sind, Math. Ann. 85 (1922), 114-139 (German).
    • (1922) Math. Ann. , vol.85 , pp. 114-139
  • 40
    • 84963105696 scopus 로고
    • On positive harmonic functions (second part)
    • S. Verblunsky, On positive harmonic functions (second part), Proc. London Math. Soc. 40 (1936), 290-320.
    • (1936) Proc. London Math. Soc. , vol.40 , pp. 290-320
    • Verblunsky, S.1
  • 42
    • 0002161530 scopus 로고
    • The Korteweg-de Vries equation is a fully integrable Hamiltonian system
    • Russian
    • V. E. Zaharov and L. D. Faddeev, The Korteweg-de Vries equation is a fully integrable Hamiltonian system, Funkcional. Anal, i Priložen. 5 (1971), no. 4, 18-27 (Russian).
    • (1971) Funkcional. Anal, I Priložen. , vol.5 , Issue.4 , pp. 18-27
    • Zaharov, V.E.1    Faddeev, L.D.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.