Logaritminės eilės begalinio indekso nehomogeninis kraštinis Rymano uždavinys sričiai, apribotai begaliniu Dini – Lipšico kontūru /

In 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.

Grantor dc:publisher

Institutional Repository of Vilnius University

Year dc:date

2009

Author dc:creator

• Spetylaitė, Jurga,

Contributors dc:contributor

• Alekna, Petras

• contour ; logaruthmic ; density ; index

Statement dc:rights

• info:eu-repo/semantics/openAccess

Language dc:language

lit

Repository record dc:identifier

https://repository.vu.lt/VU:ELABAETD1914999&prefLang=en_US

OAI identifier oai:identifier

oai:vu.lt:elaba:1914999