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Abstract
In the presented work a main Haseman type boundary value problem is investigated in the class of metaanalytic functions in the case of circular domains. With the help of Schwartz equation for circumference the initial problem can be reduced to the totality of two ordinary Haseman problems for analytic functions. Besides, the picture of solvability of the problem depending on values of indexes of coefficients of boundary value conditions is is investigated in this work.
Darbe nagrinejimas pagrindinis Hasemano tipo matanaliziniu funkciju kraštinis uždavinys H 2,M skritulineje srityje. Bet kurios srities (su glodžiu kontūru) atveju H 2,M uždavinys išnagrinetas kitame autoriaus darbe, kuriame parodyta, kad ši uždavini galima suvesti j du atskirus analiziniu funkciju uždavinius, būtent, j taip vadinamus apibendrintaji ir paprastaji Hasemano uždavinius. Šiame darbe irodyta, kad skritulines srities atveju pagrindini H 2,M uždavini galima suvesti i du atskirus iprastuosius Hasemano uždavinius analiziniu funkciju klaseje. Be to, yra parodyta, kad nagrinejamojo uždavinio išsprendžiamumas priklauso nuo kraštiniu salygu indekso.