×

zbMATH — the first resource for mathematics

Spectral theory for the wave equation with a potential term. (English) Zbl 0143.33101

PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Dunford, N., & J. Schwartz, Linear Operators, Part I. New York: Interscience 1958. · Zbl 0084.10402
[2] Goodman, R., One-sided invariant subspaces and domains of uniqueness for hyperbolic equations. Proc. Amer. Math. Soc. 15, 653-660 (1964). · Zbl 0132.35706
[3] Hille, E., & R. Phillips, Functional Analysis and Semi-groups. Amer. Math. Soc. Colloquium Publications 31, Providence 1957. · Zbl 0078.10004
[4] Ikebe, T., Eigenfunction expansions associated with the Schroedinger operators and their applications to scattering theory. Arch. Rational Mech. Anal. 5, 1-34 (1960). · Zbl 0145.36902
[5] Ikebe, T., & T. Kato, Uniqueness of the self-adjoint extension of singular elliptic differential operators. Arch. Rational Mech. Anal. 9, 77-92 (1962). · Zbl 0103.31801
[6] Jauch, J.M., Theory of the scattering operator. Helv. Phys. Acta 31, 127-158 (1958). · Zbl 0081.43304
[7] Kato, T., Fundamental properties of Hamiltonian operators of Schroedinger type. Trans. Amer. Math. Soc. 70, 195-211 (1951). · Zbl 0044.42701
[8] Kato, T., Growth properties of solutions of the reduced wave equation with a variable coefficient. Comm. Pure Appl. Math. 12, 403-425 (1959). · Zbl 0091.09502
[9] Kuroda, S.T., On the existence and unitary property of the scattering operator. Nuovo Cimento 12, 431-454 (1959). · Zbl 0084.44801
[10] Lax, P.D., & R. S. Phillips, Scattering theory. Bull. Amer. Math. Soc. 70, 130-142 (1964). · Zbl 0117.09104
[11] Lax, P.D., & R.S. Phillips, The wave equation in exterior domains. Bull. Amer. Math. Soc. 68, 47-49 (1962). · Zbl 0103.06401
[12] Povzner, A.Ya., On the expansions of arbitrary functions in terms of the eigenfunctions of the operator -?u+cu. Mat. Sbornik 32, 109-156 (1953). · Zbl 0050.32201
[13] Riesz, F., & B. Sz.-Nagy, Functional Analysis. New-York: Ungar 1955.
[14] Trotter, H., Approximation of semi-groups of operators. Pac. J. Math. 8, 887-919 (1958). · Zbl 0099.10302
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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.