Dirichlet spaces of domains bounded by quasicircles
A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä
Communications in Contemporary Mathematics, Volume 22, issue 3
AbstractConsider 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.
AVAA TIEDOSTO 12 KK EMBARGOLLA, KUN ARTIKKELI ILMESTYY
Dirichlet spaces, Faber operator, Faber series, Grunsky operator, multiply-connected domains, quasicircles
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