A+ CATEGORY SCIENTIFIC UNIT

Algebrability of the set of non-convergent Fourier series

Volume 175 / 2006

Richard M. Aron, David Pérez-García, Juan B. Seoane-Sepúlveda Studia Mathematica 175 (2006), 83-90 MSC: Primary 42A20, 46E25; Secondary 42A16. DOI: 10.4064/sm175-1-5

Abstract

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 $E$.

Authors

  • Richard M. AronDepartment of Mathematics
    Kent State University
    Kent, OH 44242, U.S.A.
    e-mail
  • David Pérez-GarcíaDepartamento de Matemática Aplicada
    E.S.C.E.T. – Universidad Rey Juan Carlos
    28933 Móstoles, Madrid, Spain
    e-mail
  • Juan B. Seoane-SepúlvedaDepartment of Mathematics
    Kent State University
    Kent, OH 44242. U.S.A.
    e-mail

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