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Algebrability of the set of non-convergent Fourier series

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Aron, Richard M. and Pérez García, David and Seoane-Sepúlveda, Juan B. (2006) Algebrability of the set of non-convergent Fourier series. Studia Mathematica, 175 (1). pp. 83-90. ISSN 0039-3223

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Official URL: http://webmail.impan.gov.pl/cgi-bin/sm/pdf?sm175-1-05



Abstract

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.


Item Type:Article
Uncontrolled Keywords:Fourier series; Divergent series; Lineability; Spaceability; Algebrability
Subjects:Sciences > Mathematics > Functional analysis and Operator theory
ID Code:20214
Deposited On:04 Mar 2013 15:34
Last Modified:25 Nov 2016 12:26

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