Abstract
This paper is devoted to singular integral operators with a linear fractional Carleman shift of arbitrary order preserving the orientation on the unit circle. The main goal is to obtain a special factorization of the operator with the help of a factorization of a related matrix function in a suitable algebra. This factorization allows us to characterize the kernel and the range of the operator under consideration, similarly to the case of singular integral operators without shift.
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Kravchenko, V.G., Lebre, A., Rodríguez, J. (2003). Factorization of Singular Integral Operators with a Carleman Shift via Factorization of Matrix Functions. In: Böttcher, A., Kaashoek, M.A., Lebre, A.B., dos Santos, A.F., Speck, FO. (eds) Singular Integral Operators, Factorization and Applications. Operator Theory: Advances and Applications, vol 142. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8007-7_11
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DOI: https://doi.org/10.1007/978-3-0348-8007-7_11
Publisher Name: Birkhäuser, Basel
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