2026-09-25T08:17:34Z https://epublications.vu.lt/oai

oai:vu.lt:elaba:1914999 2026-07-06T19:58:14Z openaireNDLTDDRIVER

Logaritminės eilės begalinio indekso nehomogeninis kraštinis Rymano uždavinys sričiai, apribotai begaliniu Dini – Lipšico kontūru /The inhomogeneous Riemann boundary - value problem with infinite index of the logarithmic order for the region limited by the infinity Dini - Lipschitz contour.Spetylaitė, Jurga,info:eu-repo/semantics/openAccesscontour ; logaruthmic ; density ; indexIn this work is formulated and studied boundary Riemann problem of logarithmic order α≥1 for the space bounded by the infinite Dini – Lipschitz contour. In this paper is used asymptotics of Cauchy type integrals with a logarithmic density. Basically differ functions Фα(z) and Фα*(z). In the first integral lnαt is contour value of the analytical function lnαz and for Cauchy-type integral Фα(z) is obtained polynomial asymptotic formula. Function Фα*(z) associated with the canonical function X(z) obtained in asymptotic formula is the only one, the fastest growing member, when z→∞. The information about the change of the Фα*(z) is insufficient considering inhomogeneous problem. It is necessary to use the Dini – Lipschitz contour. Let L΄ be Dini – Lipschitz contour of q>α order, it is proved that the function ηα(t) is continuous and bounded in contour L΄ points, and zeros of entire function F0(z) are arranged on the negative semi-axis of the real axis. Being the before mentioned contour, it was proved that a separate inhomogeneous target solution is bounded. In this work is obtained the general solution of formulated task of bounded functions in class BL.Institutional Repository of Vilnius UniversityAlekna, Petrasinfo:eu-repo/semantics/masterThesislit2009application/pdfhttps://epublications.vu.lt/object/elaba:1914999/1914999.pdfhttps://repository.vu.lt/VU:ELABAETD1914999&prefLang=en_US