Geodesic
Harmonic wavelets in a~multiply connected domain with circular boundaries
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 19 (2013) no. 1, pp. 99-114

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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.
Keywords: Schwarz problem, Dirichlet problem, harmonic wavelets, basis in spaces of harmonic functions. 
@article{TIMM_2013_19_1_a9,
     author = {G. A. Dubosarskii},
     title = {Harmonic wavelets in a~multiply connected domain with circular boundaries},
     journal = {Trudy Instituta matematiki i mehaniki},
     pages = {99--114},
     publisher = {mathdoc},
     volume = {19},
     number = {1},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TIMM_2013_19_1_a9/}
}
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G. A. Dubosarskii. Harmonic wavelets in a~multiply connected domain with circular boundaries. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 19 (2013) no. 1, pp. 99-114. http://geodesic.mathdoc.fr/item/TIMM_2013_19_1_a9/