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Reproducing Kernels for Iterated Parabolic Operators on the Upper Half Space with Application to Polyharmonic Bergman Spaces
- Source :
- Complex Analysis and Operator Theory. 11:1865-1878
- Publication Year :
- 2017
- Publisher :
- Springer Science and Business Media LLC, 2017.
-
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.
- Subjects :
- Euclidean space
Applied Mathematics
010102 general mathematics
Mathematical analysis
Poisson kernel
Hilbert space
010103 numerical & computational mathematics
Operator theory
01 natural sciences
Parabolic partial differential equation
Computational Mathematics
symbols.namesake
Computational Theory and Mathematics
Bergman space
symbols
0101 mathematics
Reproducing kernel Hilbert space
Mathematics
Bergman kernel
Subjects
Details
- ISSN :
- 16618262 and 16618254
- Volume :
- 11
- Database :
- OpenAIRE
- Journal :
- Complex Analysis and Operator Theory
- Accession number :
- edsair.doi...........06c7ba7f30dea81011e3f725f2af9268