Reproducing Kernels for Iterated Parabolic Operators on the Upper Half Space with Application to Polyharmonic Bergman Spaces |
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Authors: | Masaharu Nishio Katsunori Shimomura |
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Affiliation: | 1.Department of Mathematics,Osaka City University,Osaka,Japan;2.Department of Mathematics, Faculty of Science,Ibaraki University,Mito,Japan |
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Abstract: | 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. |
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