Eigenfunction expansions and scattering theory for perturbed elliptic partial differential operators
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- Bull. Amer. Math. Soc. 70 (1964), 517-521
References
- Felix E. Browder, Eigenfunction expansions for formally self-adjoint partial differential operators. I, II, Proc. Nat. Acad. Sci. U.S.A. 42 (1956), 769–771, 870–872. MR 92091, DOI 10.1073/pnas.42.11.870
- Felix E. Browder, Eigenfunction expansions for formally self-adjoint partial differential operators. I, II, Proc. Nat. Acad. Sci. U.S.A. 42 (1956), 769–771, 870–872. MR 92091, DOI 10.1073/pnas.42.11.870
- Felix E. Browder, The eigenfunction expansion theorem for the general self-adjoint singular elliptic partial differential operator. I. The analytical foundation, Proc. Nat. Acad. Sci. U.S.A. 40 (1954), 454–459. MR 63535, DOI 10.1073/pnas.40.6.454
- Felix E. Browder, Eigenfunction expansions for singular elliptic operators. II. The Hilbert space argument; parabolic equations on open manifolds, Proc. Nat. Acad. Sci. U.S.A. 40 (1954), 459–463. MR 63536, DOI 10.1073/pnas.40.6.459
- Lars Gårding, Eigenfunction expansions connected with elliptic differential operators, Tolfte Skandinaviska Matematikerkongressen, Lund, 1953, Lunds Universitets Matematiska Institution, Lund, 1954, pp. 44–55. MR 0071625
- Teruo Ikebe, Eigenfunction expansions associated with the Schroedinger operators and their applications to scattering theory, Arch. Rational Mech. Anal. 5 (1960), 1–34 (1960). MR 128355, DOI 10.1007/BF00252896
- Fritz John, Plane waves and spherical means applied to partial differential equations, Interscience Publishers, New York-London, 1955. MR 0075429
- Tosio Kato, On finite-dimensional perturbations of self-adjoint operators, J. Math. Soc. Japan 9 (1957), 239–249. MR 92132, DOI 10.2969/jmsj/00920239
- Tosio Kato, Fundamental properties of Hamiltonian operators of Schrödinger type, Trans. Amer. Math. Soc. 70 (1951), 195–211. MR 41010, DOI 10.1090/S0002-9947-1951-0041010-X 10. S. T. Kuroda, On the existence and unitary property of the scattering operator, Nuovo Cimento 12 (1959), 431-454.
- Shige Toshi Kuroda, Perturbation of continuous spectra by unbounded operators. I, J. Math. Soc. Japan 11 (1959), 246–262. MR 117568, DOI 10.2969/jmsj/01130247
- F. I. Mautner, On eigenfunction expansions, Proc. Nat. Acad. Sci. U.S.A. 39 (1953), 49–53. MR 52690, DOI 10.1073/pnas.39.1.49
- A. Ya. Povzner, On the expansion of arbitrary functions in characteristic functions of the operator $-\Delta u+cu$, Mat. Sbornik N.S. 32(74) (1953), 109–156 (Russian). MR 0053330
Additional Information
- Journal: Bull. Amer. Math. Soc. 70 (1964), 517-521
- DOI: https://doi.org/10.1090/S0002-9904-1964-11179-4
- MathSciNet review: 0166627