Dirichlet spaces of domains bounded by quasicircles
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A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä
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Date
2019
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en
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Communications in Contemporary Mathematics, Volume 22, issue 3
Abstract
Consider a multiply-connected domain ∑ in the sphere bounded by n non-intersecting quasicircles. We characterize the Dirichlet space of ∑ as an isomorphic image of a direct sum of Dirichlet spaces of the disk under a generalized Faber operator. This Faber operator is constructed using a jump formula for quasicircles and certain spaces of boundary values. Thereafter, we define a Grunsky operator on direct sums of Dirichlet spaces of the disk, and give a second characterization of the Dirichlet space of ∑ as the graph of the generalized Grunsky operator in direct sums of the space 1/2(1) on the circle. This has an interpretation in terms of Fourier decompositions of Dirichlet space functions on the circle.Description
AVAA TIEDOSTO 12 KK EMBARGOLLA, KUN ARTIKKELI ILMESTYY
Keywords
Dirichlet spaces, Faber operator, Faber series, Grunsky operator, multiply-connected domains, quasicircles
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Citation
Radnell, D, Schippers, E & Staubach, W 2019, ' Dirichlet spaces of domains bounded by quasicircles ', Communications in Contemporary Mathematics, vol. 22, no. 3 . https://doi.org/10.1142/S0219199719500226