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The Lebesgue Constants of Fourier Partial Sums

  • Michael I. Ganzburg
  • Elijah LiflyandEmail author
Chapter
Part of the Applied and Numerical Harmonic Analysis book series (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.

Keywords

Fourier series Partial sum Lebesgue constant Homothety 

2010 Mathematics Subject Classification

Primary 42B15; Secondary 42B05 42A05 

Notes

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.

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of HamptonHamptonUSA
  2. 2.Department of MathematicsBar-Ilan UniversityRamat-GanIsrael

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