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Rate of Convergence for Double Rational Fourier Series

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Abstract

We calculate the rate of convergence of the double rational Fourier series for regular, bounded, measurable, and two-variable functions. The rectangular oscillation of the two-variable function is used to quantify this rate. Additionally, we give an approximation of convergence rate of the double rational Fourier series for continuous functions with generalized bounded variation.

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Acknowledgements

The authors are thankful to the referee for their valuable suggestions in improving quality of the paper.

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Authors and Affiliations

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

    Hardeepbhai J. Khachar & Rajendra G. Vyas

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  1. Hardeepbhai J. Khachar
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  2. Rajendra G. Vyas
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Both the authors contributed equally.

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Correspondence to Hardeepbhai J. Khachar.

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Funding

The first author is thankful to Council of Scientific and Industrial Research, India for providing financial support through SRF (File no.: 09/0114(11228)/2021-EMR-I).

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Communicated by Tao Qian.

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Khachar, H.J., Vyas, R.G. Rate of Convergence for Double Rational Fourier Series. Complex Anal. Oper. Theory 18, 99 (2024). https://doi.org/10.1007/s11785-023-01479-w

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