Dirichlet spaces of domains bounded by quasicircles
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A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä
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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
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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