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Resonant states and poles of the scattering matrix for perturbations of - \(\Delta\). (English) Zbl 0229.35072


MSC:

35P25 Scattering theory for PDEs
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References:

[1] Shenk, N.; Thoe, D., Eigenfunction expansions and scattering theory for perturbations of −Δ, J. Math. Anal. Appl., 36, 313-351 (1971) · Zbl 0249.47004
[2] Lax, P.; Phillips, R., “Scattering Theory,” Chap. 5, Sec. 4 (1967), Academic Press: Academic Press New York · Zbl 0186.16301
[3] Rellich, F., Über das asymptotische Verhalten der Lösungen von Δu + λu = 0 in unendlichen Gebieten, Jber. Deutsch. Math. Verein., 53, 57-65 (1943) · Zbl 0028.16401
[4] Shenk, N.; Thoe, D., Outgoing solutions of (−\(Δ + q\) −\(k^2)u = f\) in an exterior domain, J. Math. Anal. Appl., 31, 81-116 (1970) · Zbl 0201.13202
[5] Yosida, K., Functional Analysis, ((1966), Springer Verlag: Springer Verlag New York/Berlin), 228 · Zbl 0217.16001
[6] Müller, C., (Spherical Harmonics, Lecture Notes in Mathematics, Vol. 17 (1966), Springer Verlag: Springer Verlag New York/Berlin) · Zbl 0138.05101
[7] Watson, G., A Treatise on the Theory of Bessel Functions (1966), Cambridge University Press: Cambridge University Press London · Zbl 0174.36202
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