广义多重傅立叶变换和连续性积分模量估算

IF 0.6 4区数学 Q3 MATHEMATICS Mathematical Notes Pub Date : 2024-07-05 DOI:10.1134/s0001434624030246

S. S. Volosivets

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引用次数: 0

摘要

摘要本文介绍了广义多重乘法傅立叶变换的性质。同时，给出了上述傅里叶变换的连续性积分模量的上界和下界，并且 \(L^2\) 中的界是不可改进的。作为推论，还得到了蒂奇马什的乘法傅里叶变换等价定理。

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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Generalized Multiple Multiplicative Fourier Transform and Estimates of Integral Moduli of Continuity

Abstract

The paper presents the properties of generalized multiple multiplicative Fourier transforms. Also, upper and lower bounds are given for the integral modulus of continuity in terms of the mentioned Fourier transforms, and the bound in \(L^2\) is unimprovable. As a corollary, an analog of Titchmarsh’s equivalence theorem for the multiplicative Fourier transform is obtained.

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来源期刊

Mathematical Notes 数学-数学

CiteScore

0.90

自引率

16.70%

发文量

179

审稿时长

24 months

期刊介绍： Mathematical Notes is a journal that publishes research papers and review articles in modern algebra, geometry and number theory, functional analysis, logic, set and measure theory, topology, probability and stochastics, differential and noncommutative geometry, operator and group theory, asymptotic and approximation methods, mathematical finance, linear and nonlinear equations, ergodic and spectral theory, operator algebras, and other related theoretical fields. It also presents rigorous results in mathematical physics.