ON THE ORDER OF MAGNITUDE OF WALSH-FOURIER TRANSFORM

被引：1

作者：

Ghodadra, Bhikha Lila ^{[1
]}

Fulop, Vanda ^{[2
]}

机构：

[1] Maharaja Sayarijao Univ Baroda, Fac Sci, Dept Math, Vadodara 390002, Gujarat, India

[2] Univ Szeged, Bolyai Inst, Aradi Vertanuk Tere 1, H-6720 Szeged, Hungary

来源：

MATHEMATICA BOHEMICA | 2020年 / 145卷 / 03期

关键词：

function of bounded variation over R+; function of bounded variation over (R+)(2); function of bounded variation over (R+()N); order of magnitude; Riemann-Lebesgue lemma; Walsh-Fourier transform; BOUNDED VARIATION; COEFFICIENTS;

D O I：

10.21136/MB.2019.0075-18

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

For a Lebesgue integrable complex-valued function f defined on R+ := [0, infinity) let (f) over cap be its Walsh-Fourier transform. The Riemann-Lebesgue lemma says that (f) over cap (y) -> 0 as y -> infinity. But in general, there is no definite rate at which the Walsh-Fourier transform tends to zero. In fact, the Walsh-Fourier transform of an integrable function can tend to zero as slowly as we wish. Therefore, it is interesting to know for functions of which subclasses of L-1(R+) there is a definite rate at which the Walsh-Fourier transform tends to zero. We determine this rate for functions of bounded variation on R+. We also determine such rate of Walsh-Fourier transform for functions of bounded variation in the sense of Vitali defined on (R+)(N), N is an element of N.

引用

页码：265 / 280

页数：16

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