完全交替函数的表征

IF 0.6 3区数学 Q2 MATHEMATICS

Journal of Approximation Theory Pub Date : 2025-08-20 DOI:10.1016/j.jat.2025.106230

Monojit Bhattacharjee , Rajkamal Nailwal

引用次数: 0

摘要

在本文中，我们用乘积半群S×Z+上的完全单调函数来表征阿贝尔半群S上的完全交替函数。我们还讨论了由一类有理函数诱导的完全交替序列，并得到了确定它们的一组充分条件（用它的零点和极点表示）。作为应用，我们给出了Z+2上由二元有理函数诱导的几类完全单调函数的完备刻划。我们还导出了序列{∏i=1k(n+ai)(n+bi)}n∈Z+,ai,bi∈(0,∞)的完全单调性的一组必要条件。

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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A characterization of completely alternating functions

In this article, we characterize completely alternating functions on an abelian semigroup

S

in terms of completely monotone functions on the product semigroup

S \times Z_{+}

. We also discuss completely alternating sequences induced by a class of rational functions and obtain a set of sufficient conditions (in terms of its zeros and poles) to determine them. As an application, we show a complete characterization of several classes of completely monotone functions on

Z_{+}^{2}

induced by rational functions in two variables. We also derive a set of necessary conditions for the complete monotonicity of the sequence

{\prod_{i = 1}^{k} \frac{(n + a_{i})}{(n + b_{i})}}_{n \in Z_{+}}, a_{i}, b_{i} \in (0, \infty)

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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.