×

zbMATH — the first resource for mathematics

Eigenfunction expansions and scattering theory for perturbations of - \(\Delta\). (English) Zbl 0249.47004

MSC:
47A40 Scattering theory of linear operators
35P10 Completeness of eigenfunctions and eigenfunction expansions in context of PDEs
47A70 (Generalized) eigenfunction expansions of linear operators; rigged Hilbert spaces
35J10 Schrödinger operator, Schrödinger equation
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Ikebe, T., Eigenfunctions expansions associated with the schroedinger operator and their applications to scattering theory, Arch. rational mech. anal., 5, 1-34, (1960) · Zbl 0145.36902
[2] Shizuta, Y., Eigenfunction expansions associated with the operator −δ in the exterior domain, (), 656-660 · Zbl 0143.14504
[3] Shenk, N., Eigenfunction expansions and scattering theory for the wave equation in an exterior region, Arch. rational mech. anal., 21, 120-150, (1966) · Zbl 0135.15602
[4] Thoe, D., Eigenfunction expansions associated with schroedinger operators in Rn, n ⩾ 4, Arch. rational mech. anal., 26, 335-356, (1967) · Zbl 0168.12501
[5] Ikebe, T., On the eigenfunction expansion connected with the exterior problem for the schroedinger equation, Japan. J. math., 36, 33-55, (1967) · Zbl 0164.13603
[6] Ikebe, T., Scattering theory for the schroedinger operator in an exterior domain, J. math. Kyoto univ., 7, 93-112, (1967) · Zbl 0153.42503
[7] Alsholm, P.; Schmidt, G., Spectral and scattering theory for schroedinger operators, () · Zbl 0226.35075
[8] Shenk, N.; Thoe, D., Outgoing solutions of \((−Δ + q − k\^{}\{2\})u = ƒ\) in an exterior region, J. math. anal. appl., 31, 81-116, (1970) · Zbl 0201.13202
[9] Ikebe, T., Orthogonality of the eigenfunctions for the exterior problem connected with −δ, Arch. rational mech. anal., 19, 71-73, (1965) · Zbl 0143.14601
[10] Shenk, N., The invariance of wave operators associated with perturbations of −δ, Journal of math. mech., 17, 1005-1022, (1968) · Zbl 0182.13202
[11] Ikebe, T., On the phase-shift formula for the scattering operator, Pacific J. math., 15, 511-523, (1965) · Zbl 0138.45004
[12] Thoe, D., Spectral theory for the wave equation with a potential term, Arch. rational. mech. anal., 22, 364-406, (1966) · Zbl 0143.33101
[13] Lax, P.D.; Phillips, R.S., Scattering theory, (1967), Academic Press New York/London · Zbl 0214.12002
[14] Goldstein, C., Eigenfunction expansions associated with the Laplacian for certain domains with infinite boundaries, Trans. amer. math. soc., 143, 283-301, (1969) · Zbl 0186.43204
[15] Hormander, L., Linear partial differential operators, (1963), Academic Press London/New York · Zbl 0171.06802
[16] Nirenberg, L., Remarks on strongly elliptic partial differential equations, Comm. pure appl. math., 13, 648-674, (1955)
[17] Agmon, S., Lectures on elliptic boundary value problems, (1965), Van Nostrand Princeton, N. J · Zbl 0151.20203
[18] Akhiezer, N.; Glazman, I., Theory of linear operators in Hilbert space, (1963), Ungar New York · Zbl 0098.30702
[19] Ikebe, T.; Kato, T., Uniqueness of the self-adjoint extension of singular elliptic differential operators, Arch. rational mech. anal., 9, 77-92, (1964) · Zbl 0103.31801
[20] Courant, R.; Hilbert, D., (), 232
[21] Dunford, N.; Schwartz, J., Linear operators, (1963), Interscience New York, Part II
[22] Hille, E.; Phillips, R., Functional analysis and semi-groups, (1957), American Mathematical Society Colloquium Publications Providence, R. I
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.