Algebrability of the set of non-convergent Fourier series

被引：81

作者：

Aron, Richard M. ^{[1
]}

Perez-Garcia, David

Seoane-Sepulveda, Juan B.

机构：

[1] Kent State Univ, Dept Math, Kent, OH 44242 USA

[2] Univ Rey Juan Carlos, ESCET, Dept Matemat Aplicada, Madrid 28933, Spain

来源：

STUDIA MATHEMATICA | 2006年 / 175卷 / 01期

关键词：

Fourier series; divergent series; lineability; spaceability; algebrability;

D O I：

10.4064/sm175-1-5

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We show that, given a set E subset of T of measure zero, the set of continuous functions whose Fourier series expansion is divergent at any point t is an element of E is dense-algebrable, i.e. there exists an infinite-dimensional, infinitely generated dense subalgebra, of C(T) every non-zero element of which has a Fourier series expansion divergent in E.

引用

页码：83 / 90

页数：8

共 12 条

[1] Lineability and spaceability of sets of functions on R [J].