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Lineability of Universal Divergence of Fourier Series

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Abstract

It is proved that large vector spaces of continuous complex functions on the unit circle exist such that all their nonzero members satisfy that, for many small subsets E of the circle, the partial sums of their Fourier series approximate any prescribed function on E. This completes or improves a number of results by several authors.

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Authors and Affiliations

  1. Departamento de Análisis Matemático, Facultad de Matemáticas, Apdo. 1160 Avda. Reina Mercedes, 41080, Seville, Spain

    Luis Bernal-González

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  1. Luis Bernal-González
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Correspondence to Luis Bernal-González.

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Dedicated to the memory of Prof. José Real Anguas, who passed away on January 2012

The author has been partially supported by the Plan Andaluz de Investigación de la Junta de Andalucía FQM-127, by Grant P08-FQM-03543, by MCI Grant MTM2009-10696-C02-01 and by MCYT Acción Especial MTM2008-02829-E.

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Bernal-González, L. Lineability of Universal Divergence of Fourier Series. Integr. Equ. Oper. Theory 74, 271–279 (2012). https://doi.org/10.1007/s00020-012-1984-6

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  • DOI: https://doi.org/10.1007/s00020-012-1984-6

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