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p08"8800<"^zEE[[[[$Explicit solutions of a singular integral equation with Carlerman shift
Edixon Rojas
University of Aveiro
Abstract
In this talk we will discuss the existence and uniqueness of solutions, as well as their explicit representation, of certain singular integral equations with Carleman shift. This will be considered within the framework of the classic Lebesgue space on a simple closed smooth curve, and the class of equations is of a type which cannot be solved by using a binomial boundary value problem. We will be able to consider some projection methodwhich allows the transformation the original equation into an equivalent simpler system of equations, reducing therefore our solvability problem to a standard scalar Riemann Hilbert problem.
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