Other Mathematics Commons^™

Bergman Spaces On Disconnected Domains, William T. Ross, Alexandru Aleman, Stefan Richter

Department of Math & Statistics Faculty Publications

For a bounded region G C C and a compact set K C G, with area measure zero, we will characterize the invariant subspaces M (under f -> zf)of the Bergman space L^p_a(G \ K), 1 ≤ p < ∞, which contain L^p_a(G) and with dim(M/(z - λ)M) = 1 for all λϵ G \ K. When G \ K is connected, we will see that di\m(M /(z — λ)M) = 1 for all λ ϵ G \ K and thus in this case we will have a complete …