关于傅立叶-迪尼展开中的尖锐热核估计值

IF 0.9 3区数学 Q2 MATHEMATICS Journal of Approximation Theory Pub Date : 2024-09-28 DOI:10.1016/j.jat.2024.106103

Bartosz Langowski , Adam Nowak

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引用次数: 0

摘要

我们证明了与（0,1）上的傅里叶-迪尼展开相关的热核的尖锐估计值，该热核配有勒贝格度量和施加于右端点的诺伊曼条件。然后，我们给出了这一结果的若干应用，包括相应泊松核和势核的尖锐边界、最大热半群和势算子的尖锐映射性质以及傅里叶-迪尼半群的边界收敛。

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On sharp heat kernel estimates in the context of Fourier–Dini expansions

We prove sharp estimates of the heat kernel associated with Fourier–Dini expansions on

(0, 1)

equipped with Lebesgue measure and the Neumann condition imposed on the right endpoint. Then we give several applications of this result including sharp bounds for the corresponding Poisson and potential kernels, sharp mapping properties of the maximal heat semigroup and potential operators and boundary convergence of the Fourier–Dini semigroup.

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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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