Abstract
The solvability of a class of singular integral equations with reflection in weighted Lebesgue spaces is analyzed, and the corresponding solutions are obtained. The main techniques are based on the consideration of certain complementary projections and operator identities. Therefore, the equations under study are associated with systems of pure singular integral equations. These systems will be then analyzed by means of a corresponding Riemann boundary value problem. As a consequence of such a procedure, the solutions of the initial equations are constructed from the solutions of Riemann boundary value problems. In the final part of the paper, the method is also applied to singular integral equations with the so-called commutative and anti-commutative weighted Carleman shifts.
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Dedicated to the memory of Professor Diómedes Bárcenas
This work was supported in part by Center for R&D in Mathematics and Applications, University of Aveiro, Portugal, through FCT—Portuguese Foundation for Science and Technology.
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Castro, L.P., Rojas, E.M. On the Solvability of Singular Integral Equations with Reflection on the Unit Circle. Integr. Equ. Oper. Theory 70, 63–99 (2011). https://doi.org/10.1007/s00020-011-1871-6
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DOI: https://doi.org/10.1007/s00020-011-1871-6