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Perturbation of resonances. (English) Zbl 0493.35037


MSC:

35J10 Schrödinger operator, Schrödinger equation
81Q15 Perturbation theories for operators and differential equations in quantum theory
35B20 Perturbations in context of PDEs
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[1] Ramm, A. G., On the analytic continuation of the solution of the Schrödinger equation in the spectral parameter and the behavior of the solution to the nonstationary problem as \(t\) → ∞, Uspeh. Mat. Nauk, 19, 192-194 (1964)
[2] Ramm, A. G., Analytical continuation of the resolvent kernel of the Schrödinger operator in the spectral parameter and limit amplitude principle in some infinite domains, Dokl. Acad. Sci. Azerb. SSR, 21, 3-7 (1965)
[3] Ramm, A. G., Sov. Phys. Dokl., 11, 673-675 (1967), [Engl. Transl.]
[4] Ramm, A. G., Some theorems on analytic continuation of the Schrödinger operator resolvent kernel in the spectral parameter, Izv. Akad. Nauk. Armjan. SSR Sec. Mat., 3, 443-464 (1968)
[5] Golubitsky, M.; Guillemin, V., Stable Mappings and Their Singularities (1973), Springer-Verlag: Springer-Verlag New York · Zbl 0294.58004
[6] Vainberg, M.; Trenogin, V., Bifuration of Solutions of Nonlinear Equations (1974), Noordhoff: Noordhoff Leiden
[7] Ramm, A. G., Nonselfadjoint operators in diffraction and scattering, Math. methods Appl. Sci., 2, 327-346 (1980) · Zbl 0437.47007
[8] Newton, R. G., Scattering of Waves and Particles (1966), McGraw-Hill: McGraw-Hill New York
[9] Ramm, A. G., A variational principle for resonances, J. Math. Phys., 21, 2052-2053 (1980) · Zbl 0452.35096
[10] Ramm, A. G.; Taylor, B. A., A new proof of absence of positive discrete spectrum of the Schrödinger operator, J. Math. Phys., 21, 2395-2397 (1980) · Zbl 0449.35020
[11] Ramm, A. G., Two sided estimates of the scattering amplitude at low energies, J. Math. Phys., 21, 308-310 (1980) · Zbl 0452.35095
[12] Kato, T., Perturbation Theory for Linear Operators (1976), Springer-Verlag: Springer-Verlag New York
[13] Howland, J., Puiseux series for resonances at an embedded eigenvalue, Pacific J. Math., 55, 157-176 (1974) · Zbl 0312.47010
[14] Simon, B., On the absorption of eigenvalues by continuous spectrum in regular perturbation problem, J. Funct. Anal., 25, 338-344 (1977) · Zbl 0363.47014
[15] Jensen, A., Local distortion technique, resonances, and poles of the \(S\)-matrix, J. Math. Anal. Appl., 59, 505-513 (1977) · Zbl 0361.47018
[16] Ramm, A. G., On exterior diffraction problems, Radiotechn. i Electron., 7, 1362-1365 (1972)
[17] Ramm, A. G., Theory and Applications of Some New Classes of Integral Equations (1980), Springer-Verlag: Springer-Verlag New York · Zbl 0456.45001
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