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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.… Click to show full 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.
Keywords:
space;
reproducing kernels;
parabolic operators;
half space;
upper half;
polyharmonic bergman
Journal Title: Complex Analysis and Operator Theory
Year Published: 2017
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Journal Title: Complex Analysis and Operator Theory
Year Published: 2017
Link to full text (if available)
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recommendations!