Sharp two-sided estimates are stated for even and odd Jacobi heat kernels on double cones and for even kernels on hyperboloids; the final comparison step in the proof is not justified.
New sharp bounds for the Jacobi heat kernel via an extension of the Dijksma-Koornwinder formula
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abstract
We obtain sharp estimates for the Jacobi heat kernel in a range of parameters where the result has not been established before. This extends and completes an earlier result due to the authors. The proof is based on a generalization of the Dijksma-Koornwinder product formula for Jacobi polynomials.
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2024 1verdicts
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Sharp estimates for Jacobi heat kernels in double conic domains
Sharp two-sided estimates are stated for even and odd Jacobi heat kernels on double cones and for even kernels on hyperboloids; the final comparison step in the proof is not justified.