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Singularities of the inverses of Fredholm operators

Published online by Cambridge University Press:  14 November 2011

A. G. Ramm
A. G. Ramm
Affiliation:
Mathematics Department, University of Manchester, Manchester M13 9PL, England
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Synopsis

Let B(k) be a linear bounded mapping of a Banach space X into a Banach space Y meromorphic in the parameter k on a connected domain of the complex plane. Under certain assumptions on B(k), more general than previously considered, the singularities of the inverse operator are described.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 102 , Issue 1-2 , 1986 , pp. 117 - 121
Copyright
Copyright © Royal Society of Edinburgh 1986

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References

1Ramm, A. G.. On the analytic continuation of the solution of the Schrödinger equation in the spectral parameter and the behaviour of the solution to the nonstationary problem for large t. Uspekhi Mat. Nauk 19 (1964), 192–194.Google Scholar
2Ramm, A. G.. On analytic continuation of the Schrödinger operator resolvent kernel in the spectral parameter. Izv. Akad. Nauk Armjan. SSR Ser. Mat. 3 (1968), 443–464.Google Scholar
3Steinberg, S.. Meromorphic families of compact operators. Arch. Rational Mech. Anal. 31 (1968), 372–379.CrossRefGoogle Scholar
4Ribaric, M. and Vidav, I.. Analytic properties of the inverse A −1(z) of an analytic operator valued function A(z). Arch. Rational Mech. Anal. 32 (1969), 298–310.CrossRefGoogle Scholar
5Dunford, N. and Schwartz, J.. Linear operators, Vol. I (New York: Wiley, 1958).Google Scholar
6Gohberg, I. and Krein, G.. Introduction to the theory of linear non-selfadjoint operators. (Providence, R.I.: Amer. Math. Soc. Transl. 18, 1969).Google Scholar
7Reed, M. and Simon, B.. Analysis of Operators (New York: Academic Press, 1978).Google Scholar
8Ramm, A. G.. Mathematical foundations of the singularity and eigenmode expansion methods. J. Math. Anal. Appl. 86 (1982), 562–591.CrossRefGoogle Scholar