DIRICHLET BOUNDARY VALUE PROBLEM IN THE WEIGHTED SPACES L^1(ρ) - Petrosyan, V.G. (Proceedings of the YSU A: Physical and Mathematical Sciences, 2017)
The Dirichlet boundary value problem in the weighted spaces L^1(ρ) on the unit circle T={z: |z|=1} is investigated, where ρ(t)=|t-t_k|^α_k , k=1,…,m, t_kT and α_k are arbitrary real numbers. The problem is to determine a function Φ(z) analytic in unit disc such that: _r→ 1-0\|ReΦ(rt)-f(t)\|_L^1(ρ_r)=0, where fL^1(ρ). In the paper necessary and sufficient conditions for solvability of the problem are given and the general solution is written in the explicit form.