Sub Hilbert spaces In the unit Ball of $\C^n$

Frédéric Symesak (1)

1 LMA [Poitiers] - Laboratoire de mathématiques et applications [UMR 6086]

Let $\Phi$ be holomorphic. We denote by $B_{\alpha}(z,w)$ the weighted Bergman Kernel. We give a condition so that the kernel $(1-\Phi(z)\overline{\Phi(w)})B-{\alpha}(z,w)$ is a reproducing kernel and we study the related Hilbert space.

Mots clés: Reproducing kernel; Sub-Bergman spaces

Domaines: Variables complexes [math.CV]

Frédéric Symesak. Sub Hilbert spaces In the unit Ball of $\C^n$. 2009. ⟨hal-00362417⟩