DISCONTINUOUS RIEMANN BOUNDARY PROBLEM IN WEIGHTED SPACES

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DISCONTINUOUS RIEMANN BOUNDARY PROBLEM IN WEIGHTED SPACES Vahee Petrosian

The Riemann boundary problem in weighted spaces L1(ρ) on T=t;|t|=1, where ρ(t)=|t−t0|α,t0∈T and α>−1, is investigated. The problem is to find analytic functions Φ+(z) and Φ−(z), Φ−(∞)=0 defined on the interior and exterior domains of T respectively, such that: limr→1−0||Φ+(rt)−a(t)Φ−(r1t)−f(t)||L1(ρ)=0, where f∈L1(ρ),a(t)∈H0(T;t1,t2,...,tm). The article gives necessary and sufficient conditions for solvability of the problem and with explicit form of thr solutions.

DOI: 10.46991/PYSU:A/2017.51.1.038 Physical and Mathematical Sciences, 51(1 (242) 38-41

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Keywords

Riemann boundary problem, weighted spaces, Cauchy type integral, Holder classes

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