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The singular spectrum of the weakly perturbed multiplication operator. (English. Russian original) Zbl 0206.43801

Funct. Anal. Appl. 4, 136-142 (1970); translation from Funkts. Anal. Prilozh. 4, No. 2, 54-61 (1970).

MSC:

47A55 Perturbation theory of linear operators
47A10 Spectrum, resolvent
47A75 Eigenvalue problems for linear operators
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References:

[1] T. Kato, Perturbation Theory for Linear Operators, Springer-Verlag, Berlin-Heidelberg-New York (1966). · Zbl 0148.12601
[2] A. I. Akhiezer and I. M. Glazman, Theory of Linear Operators in Hilbert Space [in Russian], Nauka, Moscow (1966). · Zbl 0098.30702
[3] L. D. Faddeev, ”On Friedrichs’ model in perturbation theory,” Trudy Matem. Inst. im. V. A. Steklova,30 (1964). · Zbl 0148.12801
[4] N. Aronszain, ”On Weyl’s problem,” Amer. J. Math.,79, No. 3 (1957).
[5] B. S. Pavlov, ”Uniqueness theorem for functions with positive imaginary part,” in: Problems of Mathematical Physics [in Russian], Vol. 4, LGU (1970).
[6] I. I. Privalov, Boundary Properties of Analytic Functions [in Russian], Fizmatgiz, Moscow (1956).
[7] L. Carleson, ”Sets of uniqueness for functions regular in the unit circle,” Acta Math.,87, Nos. 3-4 (1952). · Zbl 0046.30005
[8] B. S. Pavlov, ”On a non-self-adjoint Schrödinger operator. III,” in: Problems of Mathematical Physics [in Russian], No. 3, LGU (1968).
[9] B. S. Pavlov, ”On a non-self-adjoint Schrödinger operator,” in: Problems of Mathematical Physics [in Russian], Vol. 1, LGU (1966). · Zbl 0171.08602
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