Geodesic
Algebrability of the set of non-convergent Fourier series
Richard M. Aron1 ; David Pérez-García2 ; Juan B. Seoane-Sepúlveda3
1 Department of Mathematics Kent State University Kent, OH 44242, U.S.A.
2 Departamento de Matemática Aplicada E.S.C.E.T. – Universidad Rey Juan Carlos 28933 Móstoles, Madrid, Spain
3 Department of Mathematics Kent State University Kent, OH 44242. U.S.A.
Studia Mathematica, Tome 175 (2006) no. 1, pp. 83-90 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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We show that, given a set $E\subset \mathbb T$ of measure zero, the set of continuous functions whose Fourier series expansion is divergent at any point $t\in E$ is dense-algebrable, i.e. there exists an infinite-dimensional, infinitely generated dense subalgebra of $\mathcal{C}({\mathbb T})$ every non-zero element of which has a Fourier series expansion divergent in $E$.
DOI : 10.4064/sm175-1-5
Keywords: given set subset mathbb measure zero set continuous functions whose fourier series expansion divergent point dense algebrable there exists infinite dimensional infinitely generated dense subalgebra mathcal mathbb every non zero element which has fourier series expansion divergent

Richard M. Aron 1 ; David Pérez-García 2 ; Juan B. Seoane-Sepúlveda 3

1 Department of Mathematics Kent State University Kent, OH 44242, U.S.A.
2 Departamento de Matemática Aplicada E.S.C.E.T. – Universidad Rey Juan Carlos 28933 Móstoles, Madrid, Spain
3 Department of Mathematics Kent State University Kent, OH 44242. U.S.A. 
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Richard M. Aron; David Pérez-García; Juan B. Seoane-Sepúlveda. Algebrability of the set of non-convergent Fourier series. Studia Mathematica, Tome 175 (2006) no. 1, pp. 83-90. doi: 10.4064/sm175-1-5

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