About the solution in closed form of generalized markushevich boundary value problem in the class of analytical functions

    K. M. Rasulov Info

Abstract

The paper is devoted to the investigation of the problem of obtaining piecewise analytical functions F(z) = {F+(z), F (z)} with the jump line L, vanishing on the infinity and satisfying on L the boundary condition where α(t) is the preserving orientation homeomorphism of L onto itself and G(t), b(t), g(t) are given on Lfunctions of Holder class and G(t) ? 0 on L. The algorithm for the solution of this problem was obtained and particular cases, when it is solvable in closed form are determined.

Apie apibendrintojo Markuševičiaus uždavinio sprendimą analizinių funkcijų klasėje Santrauka. Darbe pateikiamas algoritmas Markuševičiaus uždavinio, kai ieškomos dalimis analizinės funkcijos F(z) = {F+ (z), F (z)} nykstančioje begalybėje, savo šuolių linijoje L tenkinančios sąlygąkur G(t), b(t), g(t) – apibrežtos kontūre L funkcijos Golderio klases, o α(t homemor‐fizmas kontūro į save. Atvejui α (t) = t uždavinį suformulavo A.I. Markuševičius 1946 m.  Įrodyta, kad uždavinio sprendimas suvedamas į integralinės antrosios rūšies Fredholmo tipo lygties sprendimą. Pateikiamas pavyzdys, iliustruojantis gautus teorinius rezultatus.

First Published Online: 14 Oct 2010

Keywords:

bianalytical function, boundary value problem, plane with slots, index

How to Cite

Rasulov, K. M. (2004). About the solution in closed form of generalized markushevich boundary value problem in the class of analytical functions. Mathematical Modelling and Analysis, 9(3), 223-228. https://doi.org/10.3846/13926292.2004.9637255

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September 30, 2004
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2004-09-30

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How to Cite

Rasulov, K. M. (2004). About the solution in closed form of generalized markushevich boundary value problem in the class of analytical functions. Mathematical Modelling and Analysis, 9(3), 223-228. https://doi.org/10.3846/13926292.2004.9637255

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