| Title |
Logaritminės eilės begalinio indekso nehomogeninis kraštinis Rymano uždavinys sričiai, apribotai begaliniu Dini – Lipšico kontūru / |
| Translation of Title |
The inhomogeneous Riemann boundary - value problem with infinite index of the logarithmic order for the region limited by the infinity Dini - Lipschitz contour. |
| Authors |
Spetylaitė, Jurga |
| Full Text |
|
| Pages |
33 |
| Keywords [eng] |
contour ; logaruthmic ; density ; index |
| Abstract [eng] |
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. |
| Type |
Master thesis |
| Language |
Lithuanian |
| Publication date |
2009 |
