平移不变核的正交扩展

IF 0.9 3区数学 Q2 MATHEMATICS Journal of Approximation Theory Pub Date : 2024-05-28 DOI:10.1016/j.jat.2024.106055

Filip Tronarp , Toni Karvonen

引用次数: 0

摘要

我们提出了一种从ℒ2(R)的正交基构造平移不变核的正交基展开的一般傅里叶分析技术。这样，我们就能在实线上推导出：(i) 以相关拉盖尔函数表示的所有半整数阶的马泰尔核，(ii) 以有理函数表示的柯西核，以及 (iii) 以赫尔米特函数表示的高斯核的显式展开。

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Orthonormal expansions for translation-invariant kernels

We present a general Fourier analytic technique for constructing orthonormal basis expansions of translation-invariant kernels from orthonormal bases of $ℒ_{2} (R)$ . This allows us to derive explicit expansions on the real line for (i) Matérn kernels of all half-integer orders in terms of associated Laguerre functions, (ii) the Cauchy kernel in terms of rational functions, and (iii) the Gaussian kernel in terms of Hermite functions.

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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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