×
Agmon, Shmuel

Spectral properties of Schrödinger operators and scattering theory. (English) Zbl 0315.47007

Ann. Sc. Norm. Super. Pisa, Cl. Sci., IV. Ser. 2, 151-218 (1975).
Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page
scan of Zbl 0315.47007

Cited in 9 Reviews
Cited in 337 Documents

MSC:

47A40 Scattering theory of linear operators
35J10 Schrödinger operator, Schrödinger equation
46E30 Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems
Cite Review PDF
Full Text: Numdam EuDML

References:

[1] S. Agmon , Lectures on elliptic boundary value problems , Van Nostrand , Math. Studies , 2 ( 1965 ). MR 178246 | Zbl 0142.37401 · Zbl 0142.37401
[2] P. Alsholm - G. Schmidt , Spectral and scattering theory for Schrödinger operators , Arch. Rational Mech. Anal. , 40 ( 1971 ), pp. 281 - 311 . MR 279631 | Zbl 0226.35076 · Zbl 0226.35076 · doi:10.1007/BF00252679
[3] N. Dunford - J.T. Schwartz , Linear operators, Part II , Interscience , New York - London , 1963 . MR 188745 | Zbl 0128.34803 · Zbl 0128.34803
[4] U. Greifenegger - K. Jörgens - J. Weidmann - M. Winkler , Streutheorie für Schrödinger-Operatoren , to appear.
[5] T. Ikebe , Eigenfunction expansions associated with the Schrödinger operators and their applications to scattering theory , Arch. Rational Mech. Anal. , 5 ( 1960 ), pp. 1 - 34 . MR 128355 | Zbl 0145.36902 · Zbl 0145.36902 · doi:10.1007/BF00252896
[6] T. Kato , Growth properties of solutions of the reduced wave equation with a variable coefficient , Comm. Pure Appl. Math. , 12 ( 1959 ), pp. 403 - 425 . MR 108633 | Zbl 0091.09502 · Zbl 0091.09502 · doi:10.1002/cpa.3160120302
[7] T. Kato , Perturbation theory for linear operators , Springer , 1966 . Zbl 0148.12601 · Zbl 0148.12601
[8] T. Kato , Some results on potential scattering , Proc. International Conf. Functional Analysis and Related Topics, Tokyo , 1969 , Tokyo University Press , 1970 , pp. 206 - 215 . MR 268713 | Zbl 0207.45303 · Zbl 0207.45303
[9] T. Kato , Scattering theory and perturbation of continuous spectra , Proc. International Congress Math. , Nice , 1970 , Gauthier-Villars , vol. 1 ( 1971 ), pp. 135 - 140 . MR 473876 | Zbl 0244.47003 · Zbl 0244.47003
[10] T. Kato , S.T. Kuroda - Theory of simple scattering and eigenfunction expansions, Functional Analysis and Related Fields , edited by F. E. Browder, Springer , 1970 , pp. 99 - 131 . MR 385603 | Zbl 0224.47004 · Zbl 0224.47004
[11] S.T. Kuroda , On the existence and the unitary property of the scattering operator , Nuovo Cimento , 12 ( 1959 ), pp. 431 - 454 . Zbl 0084.44801 · Zbl 0084.44801 · doi:10.1007/BF02745786
[12] S.T. Kuroda , Spectral representations and the scattering theory for Schrödinger operators , Proc. International Congress Math. , Nice , 1970 , Gauthier-Villars , vol. 2 ( 1971 ), pp. 441 - 445 . MR 425384 | Zbl 0241.47006 · Zbl 0241.47006
[13] S.T. Kuroda , Scattering theory for differential operators - I: Operator theory , J. Math. Soc. Japan , 25 ( 1973 ), pp. 75 - 104 . Article | MR 326435 | Zbl 0245.47006 · Zbl 0245.47006 · doi:10.2969/jmsj/02510075
[14] S.T. Kuroda , Scattering theory for differential operators - II : Self-adjoint elliptic operators , J. Math. Soc. Japan , 25 ( 1973 ), pp. 222 - 234 . Article | MR 326436 | Zbl 0252.47007 · Zbl 0252.47007 · doi:10.2969/jmsj/02520222
[15] J.L. Lions - E. Magenes , Problèmes aux limites non homogènes et applications , vol. 1 , Ed. Dunod , Paris , 1968 . MR 247243 | Zbl 0165.10801 · Zbl 0165.10801
[16] J. Milnor , Singular points of complex hypersurfaces , Ann. Math. Studies , vol. 61 , Princeton University Press and the University of Tokyo Press , Princeton , 1968 . MR 239612 | Zbl 0184.48405 · Zbl 0184.48405
[17] A. Ja. Povzner , The expansion of arbitrary functions in terms of eigenfunctions of the operator -\Delta u + cu , Math. Sbornik , 32 ( 1953 ), pp. 109 - 156 ; A.M.S. Translations , Series 2 , 60 ( 1967 ), pp. 1 - 49 . Zbl 0179.14504 · Zbl 0179.14504
[18] P.A. Rejto , Some potential perturbations of the Laplacian , Helvetica Physica. Acta , 44 ( 1971 ), pp. 708 - 736 . MR 359589
[19] M. Schechter , Spectra of partial differential operators , North Holland , 1971 . MR 447834 | Zbl 0225.35001 · Zbl 0225.35001
[20] M. Schechter , Scattering theory for elliptic operators of arbitrary order , Comm. Mat. Helvetici , 49 ( 1974 ), pp. 84 - 113 . MR 367484 | Zbl 0288.47012 · Zbl 0288.47012 · doi:10.1007/BF02566721
[21] J.R. Schulenberger - C.H. Wilcox , Eigenfunction expansions and scattering theory for wave propagation problems of classical physics , Arch. Rational Mech. Anal. , 46 ( 1972 ), pp. 280 - 320 . MR 369948 | Zbl 0252.47047 · Zbl 0252.47047 · doi:10.1007/BF00250513
[22] N. Shenk - D. Thoe , Eigenfunction expansions and scattering theory for perturbations of - \Delta , The Rocky Mountain J. of Math. , 1 ( 1971 ), pp. 89 - 125 . Zbl 0254.47017 · Zbl 0254.47017 · doi:10.1216/RMJ-1971-1-1-89
[23] D. Thoe , Eigenfunction expansions associated with Schrödinger operators in Rn, n \succcurleq 4 , Arch. Rational Mech. Anal. , 26 ( 1967 ), pp. 335 - 356 . Zbl 0168.12501 · Zbl 0168.12501 · doi:10.1007/BF00281639
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.