Toeplitz operators and weighted Bergman kernels

Details Toeplitz operators and weighted Bergman kernels Toeplitz operators and weighted Bergman kernels

2006-09-28

arxiv.org/abs/math/0609800v1

Mathematics

Functional Analysis

35 pages, no figures

Scientific paper

For a smoothly bounded strictly pseudoconvex domain, we describe the boundary singularity of weighted Bergman kernels with respect to weights behaving like a power (possibly fractional) of a defining function, and, more generally, of the reproducing kernels of Sobolev spaces of holomorphic functions of any real order. This generalizes the classical result of Fefferman for the unweighted Bergman kernel. Finally, we also exhibit a holomorphic continuation of the kernels with respect to the Sobolev parameter to the entire complex plane. Our main tool are the generalized Toeplitz operators of Boutet de Monvel and Guillemin.

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