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

    K. M. Rasulov Affiliation

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 conditionwhere 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 analizines funkcijos F(z) = {F+ (z), F (z)} nykstančioje begalybeje, savo šuoliu linijoje L tenkinančios salygakur G(t), b(t), g(t apibrežtos kontūre L funkcijos Golderio klases, o α(t homemor‐fizmas kontūro i save. Atvejui α (t) = t uždavini suformulavo A.I. Markuševičius 1946 m. Irodyta, kad uždavinio sprendimas suvedamas i integralines antrosios rūšies Fredholmo tipo lygties sprendima. Pateikiamas pavyzdys, iliustruojantis gautus teorinius rezultatus.


First Published Online: 14 Oct 2010

Keyword : 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
Published in Issue
Sep 30, 2004
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