Harmonic wavelets in a multiply connected domain with circular boundaries and their applications to problems of mathematical physics

Wavelet bases convenient for solving the Schwarz, Dirichlet, and Neumann problems in a domain with circular components of the boundary are constructed. Wavelet series converge uniformly in spaces of Hardy type. The construction of wavelets is based on a special system of harmonic rational functions to which either the Gram–Schmidt orthogonalization with respect to a special scalar product or its modification was applied.