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Local Smoothness Conditions on a Function Which Guarantee Convergence of Double Walsh-Fourier Series of This Function

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Wavelet Analysis and Applications

Part of the book series: Applied and Numerical Harmonic Analysis ((ANHA))

Abstract

The local smoothness conditions on a function are obtained, which guarantee convergence almost everywhere on some set of positive measure of the double Walsh-Fourier series of this function summed over rectangles.

This work was supported by grant 05-01-00206 of the Russian Foundation for Fundamental Research.

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Author information

Authors and Affiliations

  1. Moscow Engineering Physics Institute (State University), 31, Kashirskoe sh., Moscow, 115409, Russia

    S. K. Bloshanskaya

  2. Moscow State Regional University, 10 a, Radio Street, Moscow, 105005, Russia

    I. L. Bloshanskii

Authors
  1. S. K. Bloshanskaya
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  2. I. L. Bloshanskii
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Editor information

Editors and Affiliations

  1. Faculty of Science and Technology, University of Macau, P.O. Box 3001, Macau

    Tao Qian  & Mang I Vai  & 

  2. Department of Mathematics, Syracuse University, 215 Carnegie Hall, Syracuse, NY, 13244-1150, USA

    Yuesheng Xu

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© 2006 Birkhäuser Verlag Basel/Switzerland

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Bloshanskaya, S.K., Bloshanskii, I.L. (2006). Local Smoothness Conditions on a Function Which Guarantee Convergence of Double Walsh-Fourier Series of This Function. In: Qian, T., Vai, M.I., Xu, Y. (eds) Wavelet Analysis and Applications. Applied and Numerical Harmonic Analysis. Birkhäuser Basel. https://doi.org/10.1007/978-3-7643-7778-6_1

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