Toeplitz operators and weighted Bergman kernels

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dc.creatorEnglis, Miroslav
dc.date2006-09-28
dc.date.accessioned2026-07-07T07:25:23Z
dc.date.available2026-07-07T07:25:23Z
dc.descriptionFor 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.
dc.description35 pages, no figures
dc.identifierhttps://arxiv.org/abs/math/0609800
dc.identifierhttp://arxiv.org/abs/math/0609800
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/116697
dc.subjectFunctional Analysis
dc.subjectAnalysis of PDEs
dc.subjectComplex Variables
dc.subject32W25; 32A36, 32A25, 47B35
dc.titleToeplitz operators and weighted Bergman kernels
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