Abstract
In this paper we propose a classification to the linear-fractional shifts and consider a class of paired singular integral operators with a shift of that class. We show how the study of the this type of operators can be reduced to the study of paired operators with, what we call, a canonical shift. Some of the results obtained are used to construct explicit solutions for a class of singular integral equations with a non-Carleman shift.
Mathematics Subject Classification (2010). Primary 47G10; Secondary 47A68.
Dedicated to Professor António Ferreira dos Santos
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Campos, L., Lebre, A., Marreiros, R., Rodríguez, J. (2014). Singular Integral Operators with Linear Fractional Shifts on the Unit Circle. In: Bastos, M., Lebre, A., Samko, S., Spitkovsky, I. (eds) Operator Theory, Operator Algebras and Applications. Operator Theory: Advances and Applications, vol 242. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-0816-3_5
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DOI: https://doi.org/10.1007/978-3-0348-0816-3_5
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