Reproducing Kernels for Iterated Parabolic Operators on the Upper Half Space with Application to Polyharmonic Bergman Spaces

We consider parabolic operators of fractional order and their iterates on the upper half space of the euclidean space. We deal with Hilbert spaces of solutions of those parabolic equations. We shall show, in this note, the existence of reproducing kernels and give a formula by using their fundamenta...

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Veröffentlicht in:	Complex analysis and operator theory 2017-12, Vol.11 (8), p.1865-1878
Hauptverfasser:	Nishio, Masaharu, Shimomura, Katsunori
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Sprache:	eng
Schlagworte:	Analysis Euclidean geometry Euclidean space Hilbert space Kernels Mathematics Mathematics and Statistics Operator Theory Operators
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creator	Nishio, Masaharu Shimomura, Katsunori
description	We consider parabolic operators of fractional order and their iterates on the upper half space of the euclidean space. We deal with Hilbert spaces of solutions of those parabolic equations. We shall show, in this note, the existence of reproducing kernels and give a formula by using their fundamental solutions. As an application, we also discuss the polyharmonic Bergman spaces and give their reproducing kernels by using the Poisson kernel on the upper half space.
doi_str_mv	10.1007/s11785-017-0673-5
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title	Reproducing Kernels for Iterated Parabolic Operators on the Upper Half Space with Application to Polyharmonic Bergman Spaces
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