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On the spectra of finite-dimensional perturbations of matrix multiplication operators. (English) Zbl 0436.47042


MSC:

47Gxx Integral, integro-differential, and pseudodifferential operators
47B35 Toeplitz operators, Hankel operators, Wiener-Hopf operators
47A53 (Semi-) Fredholm operators; index theories
47A55 Perturbation theory of linear operators
45F15 Systems of singular linear integral equations
45B05 Fredholm integral equations
45P05 Integral operators
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References:

[1] A. P. CALDERON, Cauchy integrals on Lipschitz curves and related operators, Proc. Nat. Acad. Sci. USA, 74 (1977), 1324-1327 · Zbl 0373.44003 · doi:10.1073/pnas.74.4.1324
[2] I. GOHBERG and I. A. FELDMAN, Projection methods for solving Weiner-Hopf equations, English transl., Math. monographs, vol. 41, Amer. Math. Soc., Providence, R. I., 1974
[3] I. GOHBERG and M. G. KREIN, The basic propositions on defect numbers, root numbers and indices of linear operators, Uspehi Mat. Nauk, 12 (1957), 43-118; (English transl., Amer. Math. Soc. Transl., 13 (1960), 185-264
[4] I. GOHBERG and N. Ya. KRUPNIK, Introduction to the theory of one-dimensional singular integral operators, German transl., Berkhauser Verlag, Basel, 1979
[5] G. HEINIG, On the inversion and on the spectrum of Weiner-Hopf matrix operators, Math. USSR Sbornik, 20 (1973), 267-281 · Zbl 0283.47025 · doi:10.1070/SM1973v020n02ABEH001874
[6] G. HEINIG, On the inversion and on the spectrum of matrix singular integral operators, Mat. Issled. 8 (1973), 106-121. (Russian) · Zbl 0315.47022
[7] N. I. MUSKHELISHVILI, Singular integral equations. Boundary problems of function theory and their application to mathematical physics, 2nd ed., Fizmatgiz, Moscow, 1962; English transl. of 1st ed., Noordhoff, Groningen, 1953; reprinted, 1972 · Zbl 0051.33203
[8] N. P. VEKUA, Systems of singular integral equations and some boundary problems, GITTL, Moscow, 1950. English transl., Noordhoff, Groningen, 1967 · Zbl 0045.34801
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