ON POINTWISE INVERSION OF THE FOURIER TRANSFORM OF BV0 FUNCTIONS

被引：0

作者：

Mendoza Torres, Francisco J. ^{[1
]}

机构：

[1] Benemerita Univ Autonoma Puebla, Fac Cs Fis Matemat, Puebla 72570, Pue, Mexico

来源：

ANNALS OF FUNCTIONAL ANALYSIS | 2010年 / 1卷 / 02期

关键词：

Fourier transform; Henstock-Kurzweil integral; Dirichlet-Jordan theorem;

D O I：

暂无

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Using a Riemann-Lebesgue lemma for the Fourier transform over the class of bounded variation functions that vanish at infinity, we prove the Dirichlet-Jordan theorem for functions on this class. Our proof is in the Henstock-Kurzweil integral context and is different to that of Riesz-Livingston [Amer. Math. Monthly 62 (1955), 434-437]. As consequence, we obtain the Dirichlet-Jordan theorem for functions in the intersection of the spaces of bounded variation functions and of Henstock-Kurzweil integrable functions. In this intersection there exist functions in L-2(R)\L(R).

引用

页码：112 / 120

页数：9