Factorization of singular integral operators with a Carleman shift and spectral problems. (English) Zbl 1009.47034
Authors’ abstract: We study singular integral operators with a linear fractional Carleman shift preserving the orientation on the unit circle. The main goal is to characterize the spectrum of some of these operators. To this end, a special factorization of the operator is derived with the help of a factorization of a matrix function in a suitable algebra. After developing methods which permit us to obtain a factorization of a matrix function for some classes of interest, the spectral analysis of some types of singular integral operators with a Carleman shift is done.
Reviewer: Georgi E.Karadzhov (Sofia)
MSC:
| 47G10 | Integral operators |
| 47A68 | Factorization theory (including Wiener-Hopf and spectral factorizations) of linear operators |
| 47A10 | Spectrum, resolvent |
Keywords:
singular integral operators; factorization; spectral problems; linear fractional Carleman shiftReferences:
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