Sharp estimates for Jacobi heat kernels in conic domains

IF 0.9 3区数学 Q2 MATHEMATICS Journal of Approximation Theory Pub Date : 2023-09-01 DOI:10.1016/j.jat.2023.105921

Dawid Hanrahan , Dariusz Kosz

引用次数: 0

Abstract

We prove genuinely sharp estimates for the Jacobi heat kernels introduced in the context of the multidimensional cone $V^{d + 1}$ and its surface $V_{0}^{d + 1}$ . 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.

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二次域Jacobi热核的尖锐估计

我们证明了在多维锥Vd+1及其表面V0d+1的背景下引入的Jacobi热核的真正尖锐的估计。为此，我们将徐探索的圆锥上的雅可比多项式理论与诺瓦克、舍格伦和萨雷克最近开发的技术相结合，这些技术旨在找到球面热核的真正尖锐的估计。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of Approximation Theory 数学-数学

CiteScore

1.90

自引率

11.10%

发文量

审稿时长

6-12 weeks

期刊介绍： The Journal of Approximation Theory is devoted to advances in pure and applied approximation theory and related areas. These areas include, among others: • Classical approximation • Abstract approximation • Constructive approximation • Degree of approximation • Fourier expansions • Interpolation of operators • General orthogonal systems • Interpolation and quadratures • Multivariate approximation • Orthogonal polynomials • Padé approximation • Rational approximation • Spline functions of one and several variables • Approximation by radial basis functions in Euclidean spaces, on spheres, and on more general manifolds • Special functions with strong connections to classical harmonic analysis, orthogonal polynomial, and approximation theory (as opposed to combinatorics, number theory, representation theory, generating functions, formal theory, and so forth) • Approximation theoretic aspects of real or complex function theory, function theory, difference or differential equations, function spaces, or harmonic analysis • Wavelet Theory and its applications in signal and image processing, and in differential equations with special emphasis on connections between wavelet theory and elements of approximation theory (such as approximation orders, Besov and Sobolev spaces, and so forth) • Gabor (Weyl-Heisenberg) expansions and sampling theory.

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