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Reconstruction of Functions via Walsh-Fourier Cofficients

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Computer Aided Systems Theory – EUROCAST 2011 (EUROCAST 2011)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6928))

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Abstract

It is of main interest in the theory and also in applications of Fourier series that how to reconstruct a function from the partial sums of its Walsh-Fourier series. In 1955 Fine proved the Fejér-Lebesgue theorem, that is for each integrable function we have the almost everywhere convergence of Fejér means σ n f → f. It is also of prior interest that what can be said - with respect to this reconstruction issue - if we have only a subsequence of the partial sums. In this paper we give a brief résumé of the recent results with respect to this issue above also regarding the class of two-variable integrable functions.

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Authors and Affiliations

  1. College of Nyíregyháza, Inst. of Math. and Comp. Sci., Nyíregyháza, P.O. Box 166, H–4400, Hungary

    György Gát

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  1. György Gát
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Roberto Moreno-Díaz Franz Pichler Alexis Quesada-Arencibia

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Gát, G. (2012). Reconstruction of Functions via Walsh-Fourier Cofficients. In: Moreno-Díaz, R., Pichler, F., Quesada-Arencibia, A. (eds) Computer Aided Systems Theory – EUROCAST 2011. EUROCAST 2011. Lecture Notes in Computer Science, vol 6928. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-27579-1_45

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  • DOI: https://doi.org/10.1007/978-3-642-27579-1_45

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-27578-4

  • Online ISBN: 978-3-642-27579-1

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