Reproducing kernel Hilbert spaces supporting nontrivial Hermitian weighted composition operators

Details Reproducing kernel Hilbert spaces supporting nontrivial Hermitian weighted composition operators Reproducing kernel Hilbert spaces supporting nontrivial Hermitian weighted composition operators

2011-04-07

arxiv.org/abs/1104.1329v1

Mathematics

Functional Analysis

14 pages

Scientific paper

We characterize those generating functions k that produce weighted Hardy spaces of the unit disk D supporting nontrivial Hermitian weighted composition operators. Our characterization shows that the spaces associated with the "classical reproducing kernels," as well as certain natural extensions of these spaces, are precisely those that are hospitable to Hermitian weighted composition operators. It also leads to a refinement of a necessary condition for a weighted composition to be Hermitian, obtained recently by Cowen, Gunatillake, and Ko, into one that is both necessary and sufficient.

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