On the reproducing kernel of the Segal-Bargmann space

This article revolves around the properties on the L p scale of spaces of the integral kernel operator K whose kernel function is the reproducing kernel of the Segal-Bargmann space. We find sufficient conditions on p and q for K to be a Hille-Tamarkin (and hence compact) operator from L p to L q wit...

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Bibliographic Details
Published in:Journal of mathematical physics 1999-03, Vol.40 (3), p.1664-1676
Main Author: Sontz, Stephen Bruce
Format: Article
Language:English
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Summary:This article revolves around the properties on the L p scale of spaces of the integral kernel operator K whose kernel function is the reproducing kernel of the Segal-Bargmann space. We find sufficient conditions on p and q for K to be a Hille-Tamarkin (and hence compact) operator from L p to L q with respect to the standard Gaussian measure as well as with respect to a weighted measure on the codomain space. We also find sufficient conditions for K to be unbounded with respect to the standard Gaussian measure. Finally we give sufficent conditions for a Toeplitz operator to be Hille-Tamarkin on the L p scale of spaces with respect to both the standard Gaussian measure and a weighted measure on the codomain space.
ISSN:0022-2488
1089-7658
DOI:10.1063/1.532824