A Forelli-Rudin construction and asymptotics of weighted Bergman kernels (Q1593732)

Let \(\Omega\subset\mathbb C^N\) be pseudoconvex with smooth boundary and let \(-\phi\), \(-\psi\) be smooth defining functions for \(\Omega\) with \(\log\phi\), \(\log\psi\) being plurisubharmonic in \(\Omega\). Let \(M\geq 0\). The author investigates the asymptotic behavior of the weighted Bergman kernel \(K_{\phi^k\psi^M}\) as \(k\rightarrow\infty\).