Abstract
The eigenvalue of nonpositive type of a π-selfadjoint operator A in a Pontrjagin space of index one is characterized in a model of A. Similar questions are studied for an eigen-value problem λG-T in a Hilbert space with a selfadjoint operator T and a special operator G.
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References
Aronszajn, N. and Donoghue, W.F.: On exponential representations of analytic functions in the per half-plane with positive imaginary part, J. d'Analyse Math. 5 (1956–57), 321–388.
Ball, J.A. and Greenberg, W.: A Pontrjagin space analysis of the supercritical transport equation, Transport Theory and Statistical Physics 4 (1975), 143–154.
Bognár, J.: Indefinite inner product spaces, Berlin 1974.
Case, K.M. and Zweifel, P.F.: Linear transport theory, Reading, Mass. 1967.
Jochvidov, I.S.; Krein, M.G.; Langer H.: Introduction to the spectral theory of operators in spaces with an indefinite metric, Berlin 1982.
Jonas, P.: Compact perturbations of definitizable operators II, J. Operator Theory 8 (1982), 3–18.
Jonas, P. and Langer, H.: Some questions in the perturbation theory of J-nonnegative operators in Krein spaces, Math. Nachr. 114 (1983), 205–226.
Kac, I.S. and Krein, M.G.: R-functions-analytic functions mapping the per halfplane into itself, Amer. Math. Soc. Transl. 103 (1974), 1–18.
Krein, M.G. and Langer, H.: On the spectral function of a selfadjoint operator in a space with indefinite metric, Dokl. Akad. Nauk SSSR 152 (1963), 39–42 (Russian).
Krein, M.G. and Langer, H.: Über einige Fortsetzungsprobleme, die eng mit der Theorie hermitescher Operatoren im Raume Π x zusammenhängen. I. Einige Funktionenklassen und ihre Darstellungen, Math. Nachr. 77 (1977), 187–236.
Krein, M.G. and Langer, H.: Some propositions on analytic matrix functions related to the theory of operators in the space Π x , Acta Sci. Math. 43 (1981), 181–205.
Krein, M.G. and Šmul'jan, Ju.L.: Wiener-Hopf equations whose kernels admit an integral representation with the exponential function, Izv. Akad. Nauk Armjan. SSR 17 (1982), 307–327 (Russian).
Langer, H.: Zur Spektral theorie J-selbstadjungierter Operatoren, Dissertation, Technische Universität Dresden 1960.
Langer, H.: On J-hermitian operators, Dokl. Akad. Nauk SSSR 134 (1960), 263–266 (Russian).
Langer, H.: Spectral functions of definitizable operators in Krein spaces, Functional analysis, Proceedings, Dubrovnik 1981, Lecture Notes in Mathematics 948, Berlin 1982.
Markuševič, A.I.: Theory of analytic functions, Moscou 1968 (Russian).
Mee, C.V.M. van der: Semigroup and factorization methods in transport theory, Mathematical centre tracts 146, Amsterdam 1981.
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Jonas, P., Langer, H. A model for π-selfadjoint operators in π1 and a special linear pencil. Integr equ oper theory 8, 13–35 (1985). https://doi.org/10.1007/BF01199980
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DOI: https://doi.org/10.1007/BF01199980