Proper holomorphic liftings and new formulas for the Bergman and Szegő kernels
Volume 152 / 2002
Studia Mathematica 152 (2002), 161-186
MSC: 32A25, 32H35.
DOI: 10.4064/sm152-2-5
Abstract
We consider a large class of convex circular domains in $M_{m_{1}, n_{1}}({\mathbb C})\times \dots\times M_{m_{d}, n_{d}}({\mathbb C})$ which contains the oval domains and minimal balls. We compute their Bergman and Szeg{ő} kernels. Our approach relies on the analysis of some proper holomorphic liftings of our domains to some suitable manifolds.
