Functional Analysis and Applications Seminar 

09/07/2010, 15:00 — 16:00 — Room P3.10, Mathematics Building
Luís Pessoa, Instituto Superior Técnico, UT Lisboa

Poly-Bergman spaces on domains Möbius-equivalent to a disk

Let $U$ be a complex domain Möbius-equivalent to a disk and let $j$ be a non zero integer. The talk will focus on explicit representation of the poly-Bergman projection of order $j$, in terms of the canonical two-dimensional singular integral operators. One also shows how the Lebesgue space $L^2(U;\mathrm{dA})$ decomposes on the true poly-Bergman spaces, where $\mathrm{dA}$ is the element of Lebesgue area measure. The poly-Bergman kernels of $U$ are explicitly calculated.