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Boundary value problems and singular integral equations on Banach function spaces

Volume 512 / 2015

E. M. Rojas Dissertationes Mathematicae 512 (2015), 1-42 MSC: Primary 30E25, 46E30; Secondary 42B20, 47B38. DOI: 10.4064/dm742-12-2015 Published online: 14 December 2015

Abstract

We study the solvability and Fredholmness of binomial boundary value problems for analytic functions represented by integrals of Cauchy type with density on abstract nonstandard Banach function spaces, assuming continuous, piecewise continuous and essentially bounded factorizable functions as coefficients. The representation of the solutions of those problems allows us to describe the explicit form of the solutions of the associated singular integral equations in each case. The solvability and explicit representation of the solutions of a class of singular integral equations with Carleman shifts is also considered.

Authors

  • E. M. RojasDepartamento de Matem\'aticas
    Universidad Nacional de Colombia
    Carrera 30 No. 45-03
    11321, Bogot\'a, Colombia
    e-mail

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