-
1
-
-
0000545486
-
On semi-classical bounds for eigenvalues of Schrödinger operators
-
10.1016/0375-9601(78)90385-7
-
Aizenman M. Lieb E.H. On semi-classical bounds for eigenvalues of Schrödinger operators. Phys. Lett. A 1978, 66:427-429. 10.1016/0375-9601(78)90385-7
-
(1978)
Phys. Lett. A
, vol.66
, pp. 427-429
-
-
Aizenman, M.1
Lieb, E.H.2
-
2
-
-
84872960762
-
Fractional calculus in hydrologic modeling: A numerical perspective
-
10.1016/j.advwatres.2012.04.005
-
Benson D.A. Meerschaert M.M. Revielle J. Fractional calculus in hydrologic modeling: A numerical perspective. Adv. Water Resour. 2013, 51:479-497. 10.1016/j.advwatres.2012.04.005
-
(2013)
Adv. Water Resour.
, vol.51
, pp. 479-497
-
-
Benson, D.A.1
Meerschaert, M.M.2
Revielle, J.3
-
3
-
-
84931493237
-
Covariant and contravariant symbols of operators
-
10.1070/IM1972v006n05ABEH001913, (in Russian);, (English translation).
-
Berezin F. Berezin F. Covariant and contravariant symbols of operators. Math. USSR, Izv. 1972, 6:1117-1151. 10.1070/IM1972v006n05ABEH001913, (in Russian);, (English translation).
-
(1972)
Math. USSR, Izv.
, vol.6
, pp. 1117-1151
-
-
Berezin, F.1
Berezin, F.2
-
4
-
-
84972491111
-
The asymptotic distribution of the eigenvalues for a class of Markov operators
-
10.2140/pjm.1959.9.399
-
Blumenthal R. Getoor R. The asymptotic distribution of the eigenvalues for a class of Markov operators. Pac. J. Math. 1959, 9:399-408. 10.2140/pjm.1959.9.399
-
(1959)
Pac. J. Math.
, vol.9
, pp. 399-408
-
-
Blumenthal, R.1
Getoor, R.2
-
5
-
-
55349101942
-
Hardy-Lieb-Thirring inequalities for fractional Schrödinger operators
-
10.1090/S0894-0347-07-00582-6
-
Frank R.L. Lieb E.H. Seiringer R. Hardy-Lieb-Thirring inequalities for fractional Schrödinger operators. J. Am. Math. Soc. 2008, 21:925-950. 10.1090/S0894-0347-07-00582-6
-
(2008)
J. Am. Math. Soc.
, vol.21
, pp. 925-950
-
-
Frank, R.L.1
Lieb, E.H.2
Seiringer, R.3
-
6
-
-
79960343156
-
-
Mathematical Results in Quantum Physics, Proceedings of the QMath 11 Conference, Hradec Kralove, Czech Republic, 6-10 September 2010 (World Scientific Publishing, Hackensack, NJ)
-
Frank R.L. Geisinger L. Two-Term Spectral Asymptotics for the Dirichlet Laplacian on a Bounded Domain 2011, 138-147. and Mathematical Results in Quantum Physics, Proceedings of the QMath 11 Conference, Hradec Kralove, Czech Republic, 6-10 September 2010 (World Scientific Publishing, Hackensack, NJ)
-
(2011)
Two-Term Spectral Asymptotics for the Dirichlet Laplacian on a Bounded Domain
, pp. 138-147
-
-
Frank, R.L.1
Geisinger, L.2
-
7
-
-
84886856405
-
-
In our notation, α = 2s.
-
In our notation, α = 2s.
-
-
-
-
8
-
-
84886840789
-
-
m)thomampersan
-
m)ψ)(x)|<∞.
-
-
-
-
9
-
-
84886852093
-
-
The ℏ dependence of the operator L will be declared explicitly when needed. Also the coefficient ℏ2/2m of the kinetic term has been simplified by setting m = [M]/2. Thus, the dimensions of the constant factor are [M][L]4/[T]2 for s = 1.
-
The ℏ dependence of the operator L will be declared explicitly when needed. Also the coefficient ℏ2/2m of the kinetic term has been simplified by setting m = [M]/2. Thus, the dimensions of the constant factor are [M][L]4/[T]2 for s = 1.
-
-
-
-
10
-
-
84886868105
-
-
2.
-
2.
-
-
-
-
11
-
-
84886858551
-
-
The (d - 1)-dimensional Minkowski content of ∂Ω is defined as in Ref. 20
-
320. The (d - 1)-dimensional Minkowski content of ∂Ω is defined as in Ref. 20
-
-
-
-
13
-
-
80051683101
-
On Riesz means of eigenvalues
-
10.1080/03605302.2011.595865
-
Harrel E.M. Hermi L. On Riesz means of eigenvalues. Commun. Partial Differ. Equ. 2011, 36:1521-1543. 10.1080/03605302.2011.595865
-
(2011)
Commun. Partial Differ. Equ.
, vol.36
, pp. 1521-1543
-
-
Harrel, E.M.1
Hermi, L.2
-
14
-
-
0002661764
-
Second term of the spectral asymptotic expansion of the Laplace-Beltrami operator on manifolds with boundary
-
10.1007/BF01086550
-
Ivrii V.Y. Second term of the spectral asymptotic expansion of the Laplace-Beltrami operator on manifolds with boundary. Funct. Anal. Appl. 1980, 14(2):98-106. 10.1007/BF01086550.
-
(1980)
Funct. Anal. Appl.
, vol.14
, Issue.2
, pp. 98-106
-
-
Ivrii, V.Y.1
-
15
-
-
0002697827
-
Can one hear the shape of a drum?
-
10.2307/2313748
-
Kac M. Can one hear the shape of a drum?. Am. Math. Monthly 1966, 73:1-23. 10.2307/2313748.
-
(1966)
Am. Math. Monthly
, vol.73
, pp. 1-23
-
-
Kac, M.1
-
16
-
-
15244359871
-
-
Mathematical Surveys and Monographs. (AMS, Providence, RI).
-
Koldobsky A. Fourier Analysis in Convex Geometry 2005, 116. Mathematical Surveys and Monographs Vol. (AMS, Providence, RI).
-
(2005)
Fourier Analysis in Convex Geometry
, vol.116
-
-
Koldobsky, A.1
-
17
-
-
0031574602
-
Dirichlet and Neumann eigenvalue problems on domains in Euclidean spaces
-
10.1006/jfan.1997.3155
-
Laptev A. Dirichlet and Neumann eigenvalue problems on domains in Euclidean spaces. J. Funct. Anal. 1997, 151:531-545. 10.1006/jfan.1997.3155.
-
(1997)
J. Funct. Anal.
, vol.151
, pp. 531-545
-
-
Laptev, A.1
-
18
-
-
0002983823
-
Sharp Lieb-Thirring inequalities in high dimensions
-
10.1007/BF02392782
-
Laptev A. Weidl T. Sharp Lieb-Thirring inequalities in high dimensions. Acta Math. 2000, 184:87-111. 10.1007/BF02392782
-
(2000)
Acta Math.
, vol.184
, pp. 87-111
-
-
Laptev, A.1
Weidl, T.2
-
19
-
-
0000538029
-
On the Schrödinger equations and the eigenvalue problem
-
10.1007/BF01213210
-
Li P. Yau S.T. On the Schrödinger equations and the eigenvalue problem. Commun. Math. Phys. 1983, 88:309-318. 10.1007/BF01213210
-
(1983)
Commun. Math. Phys.
, vol.88
, pp. 309-318
-
-
Li, P.1
Yau, S.T.2
-
20
-
-
0004148844
-
-
Graduate Studies in Mathematics. (AMS, Providence, RI).
-
Lieb E.H. Loss M. Analysis 2010, 14. and Graduate Studies in Mathematics Vol. (AMS, Providence, RI).
-
(2010)
Analysis
, vol.14
-
-
Lieb, E.H.1
Loss, M.2
-
21
-
-
0002020225
-
Weyl's conjecture for manifolds with concave boundary
-
10.1090/pspum/036
-
Melrose R. Weyl's conjecture for manifolds with concave boundary. Proc. Symp. Pure Math. 1980, 36:257-274. 10.1090/pspum/036.
-
(1980)
Proc. Symp. Pure Math.
, vol.36
, pp. 257-274
-
-
Melrose, R.1
-
22
-
-
84855892829
-
Eigenvalues of the fractional Laplace operator in the interval
-
10.1016/j.jfa.2011.12.004
-
Kwaśnicki M. Eigenvalues of the fractional Laplace operator in the interval. J. Funct. Anal. 2012, 262:2379-2402. 10.1016/j.jfa.2011.12.004.
-
(2012)
J. Funct. Anal.
, vol.262
, pp. 2379-2402
-
-
Kwaśnicki, M.1
-
23
-
-
84863469913
-
Hitchhiker's guide to the fractional Sobolev spaces
-
10.1016/j.bulsci.2011.12.004
-
Di Nezza E. Palatucci G. Valdinoci E. Hitchhiker's guide to the fractional Sobolev spaces. Bull. Sci. Math. 2012, 136:521-573. 10.1016/j.bulsci.2011.12.004
-
(2012)
Bull. Sci. Math.
, vol.136
, pp. 521-573
-
-
Di Nezza, E.1
Palatucci, G.2
Valdinoci, E.3
-
25
-
-
84963097105
-
On the eigenvalues of the vibrating membranes
-
10.1112/plms/s3-11.1.419
-
Pólya G. On the eigenvalues of the vibrating membranes. Proc. London Math. Soc. 1961, 11(3):419-433. 10.1112/plms/s3-11.1.419.
-
(1961)
Proc. London Math. Soc.
, vol.11
, Issue.3
, pp. 419-433
-
-
Pólya, G.1
-
27
-
-
0242593273
-
A new coherent states approach to semiclassics which gives Scott's correction
-
10.1007/s00220-003-0936-z
-
Solovej J.P. Spitzer W.L. A new coherent states approach to semiclassics which gives Scott's correction. Commun. Math. Phys. 2003, 241:383-420. 10.1007/s00220-003-0936-z
-
(2003)
Commun. Math. Phys.
, vol.241
, pp. 383-420
-
-
Solovej, J.P.1
Spitzer, W.L.2
-
28
-
-
0001117305
-
Das asymptotische Verteilungsgesetz der Eigenwerte linearer partieller Differentialgleichungen (mit einet Anwendung auf die Theorie der Hohlraumstrahlung)
-
10.1007/BF01456804
-
Weyl H. Das asymptotische Verteilungsgesetz der Eigenwerte linearer partieller Differentialgleichungen (mit einet Anwendung auf die Theorie der Hohlraumstrahlung). Math. Ann. 1912, 71:441-479. 10.1007/BF01456804.
-
(1912)
Math. Ann.
, vol.71
, pp. 441-479
-
-
Weyl, H.1
-
29
-
-
0039180579
-
Über die Abhängigkeit der Eigenschwingungen einer Membran von deren Begrenzung
-
Weyl H. Über die Abhängigkeit der Eigenschwingungen einer Membran von deren Begrenzung. J. Reine Angew. Math. 1912, 141:1-11.
-
(1912)
J. Reine Angew. Math.
, vol.141
, pp. 1-11
-
-
Weyl, H.1
-
30
-
-
84871436168
-
Über das Spektrum der Hohlraumstrahlung
-
Weyl H. Über das Spektrum der Hohlraumstrahlung. J. Reine Angew. Math. 1912, 141:163-181.
-
(1912)
J. Reine Angew. Math.
, vol.141
, pp. 163-181
-
-
Weyl, H.1
-
31
-
-
84914015516
-
Über die Randwertaufgabe der Strahlungstheorie und asymptotische Spektralgeometrie
-
Weyl H. Über die Randwertaufgabe der Strahlungstheorie und asymptotische Spektralgeometrie. J. Reine Angew. Math. 1913, 143:177-202
-
(1913)
J. Reine Angew. Math.
, vol.143
, pp. 177-202
-
-
Weyl, H.1
|