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Exploring the spectra of some classes of singular integral operators with symbolic computation. (English) Zbl 1380.47038

The paper shows the possibilities of the Mathematica computer algebra system to explore the spectra of several classes of singular integral operators. For a singular integral operator with rational coefficients, a pseudo code is given which permits to check if a given complex number is in the spectrum of the given operator. The matrix case is also discussed. Singular integral operators with essentially bounded coefficients of some special type are investigated. The paper contains numerous examples.

MSC:

47G10 Integral operators
47A10 Spectrum, resolvent
47A68 Factorization theory (including Wiener-Hopf and spectral factorizations) of linear operators
68W30 Symbolic computation and algebraic computation
45P05 Integral operators
45E05 Integral equations with kernels of Cauchy type
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