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The Lebesgue Constants of Fourier Partial Sums

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Book cover Topics in Classical and Modern Analysis

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

Abstract

We give a brief overview of the results on the behavior of the Lebesgue constants for various partial sums of multiple Fourier series. In addition, we establish a new property of the Lebesgue constants concerning its partly increasing behavior.

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Acknowledgements

The authors acknowledge the support of the Gelbart Institute at the Mathematics Department in Bar-Ilan University.

The authors are indebted to the referee for thorough reading and valuable remarks and suggestions.

Last but not least, the authors thank A. Podkorytov for bringing their attention to Szegö’s result and for interesting discussions.

Author information

Authors and Affiliations

  1. Department of Mathematics, University of Hampton, Hampton, VA, USA

    Michael I. Ganzburg

  2. Department of Mathematics, Bar-Ilan University, Ramat-Gan, Israel

    Elijah Liflyand

Authors
  1. Michael I. Ganzburg
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  2. Elijah Liflyand
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Correspondence to Elijah Liflyand .

Editor information

Editors and Affiliations

  1. Georgia Southern University, Statesboro, GA, USA

    Martha Abell

  2. Georgia Southern University, Statesboro, GA, USA

    Emil Iacob

  3. Georgia Southern University, Statesboro, GA, USA

    Alex Stokolos

  4. Georgia Southern University, Statesboro, GA, USA

    Sharon Taylor

  5. ICREA, Passeig de Lluís Companys, Barcelona, Spain ; Centre de Recerca Matemàtica, Barcelona, Spain

    Sergey Tikhonov

  6. Georgia Southern University, Statesboro, GA, USA

    Jiehua Zhu

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Ganzburg, M.I., Liflyand, E. (2019). The Lebesgue Constants of Fourier Partial Sums. In: Abell, M., Iacob, E., Stokolos, A., Taylor, S., Tikhonov, S., Zhu, J. (eds) Topics in Classical and Modern Analysis. Applied and Numerical Harmonic Analysis. Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-12277-5_10

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