Harmonic wavelets in a multiply connected domain with circular boundaries

A new approach to the solution of the Schwarz and Dirichlet problems in a domain with circular components of the boundary is proposed. The convergence rate is studied for the series that represent a solution in spaces of Hardy type and converge uniformly for smooth boundary values. Examples of functions for which the constructed series diverge are presented. Harmonic wavelets are constructed such that series in these wavelets converge for all functions from the considered spaces.