On the solvability of singular integral equations with reflection on the unit circle
The paper is organized in seven sections. References are exhaustive and these citations can initiate furthering the research in the directions similar to those given in the paper but with different approach. The fundamental concept that helped the authors to write this paper is the formulation of linear boundary value problems for analytic functions. Singular integral equations with shift are connected with boundary value problems with a shift in a natural way. With all knowledge on these and similar topics and several applications and theories developed, the authors are inspired to reduce a class of singular integral equations with shift on a weighted Lebesgue space to a system of singular integral equations by using some operator identities and projections, by which the solutions of the initial equation throughout a Riemann boundary value problem are studied. The authors avoid the use of the classical method, which allows a direct construction of the corresponding solutions. Therefore, the equations under study are associated with a system of pure singular integral equations. In the final part of the paper weighted Carleman shift operators of commutative and anti-commutative types are considered.
scientific article; zbMATH DE number 5909271
scientific article