Skip to main content
SpringerLink
Log in

A note on multiple rational Fourier series

  • Published:
Periodica Mathematica Hungarica Aims and scope Submit manuscript

Abstract

The multiple rational Fourier series is defined and the multiple rational Fourier coefficients are studied for functions of \({\text {Lip}}(p;\alpha _1,\alpha _2, \ldots ,\alpha _N)\) class and \(\varPhi \)-\(\varLambda \)-bounded variation in sense of Vitali and Hardy.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. J. Bokor, F. Schipp, Approximate identification in Laguerre and Kautz bases. Automatica 34, 463–468 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  2. V. Fülöp, F. Móricz, Order of magnitude of multiple Fourier coefficients of functions of bounded variation. Acta Math. Hung. 104, 95–104 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  3. L. Tan, C. Zhou, On the order of rational Fourier coefficients. Complex Var. Elliptic Equ. 58, 1737–1743 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  4. R.G. Vyas, On the absolute convergence of Fourier series of functions of \(\Lambda BV^{(p)}\) and \(\varphi \lambda BV\). Georgian Math. J. 14, 769–774 (2001)

    Article  MathSciNet  Google Scholar 

  5. R.G. Vyas, K.N. Darji, Order of magnitude of multiple Fourier coefficients. Anal. Theory Appl. 29, 27–36 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  6. R.G. Vyas, K.N. Darji, On multiple Fourier coefficients of functions of \(\phi \)-\(\Lambda \)-bounded variation. Math. Inequalities Appl. 17, 1153–1160 (2014)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Acknowledgements

The first author would like to thank Council of Scientific & Industrial Research (CSIR) for the financial assistant through JRF (File no.: 09/0114(11228)/2021-EMR-I). The authors are thankful to the referees for their valuable suggestions.

Author information

Authors and Affiliations

  1. Department of Mathematics Faculty of science, The Maharaja Sayajirao University of Baroda, Vadodara, 390002, India

    H. J. Khachar & R. G. Vyas

Authors
  1. H. J. Khachar
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. R. G. Vyas
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Khachar, H.J., Vyas, R.G. A note on multiple rational Fourier series. Period Math Hung 85, 264–274 (2022). https://doi.org/10.1007/s10998-021-00433-7

Download citation

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10998-021-00433-7

Keywords

Mathematics Subject Classification

Search

Navigation