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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; Ramm, A.G, Domain where the resonances are absent in the three-dimensional scattering problem, Doklady, 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 New York · Zbl 0294.58004
[6] Vainberg, M; Trenogin, V, Bifuration of solutions of nonlinear equations, (1974), 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 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 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 New York · Zbl 0456.45001
[18] {\scA. G. Ramm}, Mathematical foundations of the singularity and eigenmode expansion methods (SEM and EEM), J. Math. Anal. Appl.{\bf86}, 562-591. · Zbl 0486.35065
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