Sharp estimates for Jacobi heat kernels in conic domains

We prove genuinely sharp estimates for the Jacobi heat kernels introduced in the context of the multidimensional cone Vd+1 and its surface V0d+1. To do so, we combine the theory of Jacobi polynomials on the cone explored by Xu with the recent techniques by Nowak, Sjögren, and Szarek, developed to fi...

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Bibliographic Details
Published in:	Journal of approximation theory Vol. 293; p. 105921
Main Authors:	Hanrahan, Dawid, Kosz, Dariusz
Format:	Journal Article
Language:	English
Published:	Elsevier Inc 01-09-2023
Subjects:	Jacobi heat kernel Multidimensional cone Multidimensional cone Jacobi heat kernel primary
Online Access:	Get full text
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Summary:	We prove genuinely sharp estimates for the Jacobi heat kernels introduced in the context of the multidimensional cone Vd+1 and its surface V0d+1. To do so, we combine the theory of Jacobi polynomials on the cone explored by Xu with the recent techniques by Nowak, Sjögren, and Szarek, developed to find genuinely sharp estimates for the spherical heat kernel.
ISSN:	0021-9045 1096-0430
DOI:	10.1016/j.jat.2023.105921