

Rate of convergence of double rational Fourier series of functions of generalized bounded variation
https://doi.org/10.26907/0021-3446-2025-5-26-43
Abstract
The rate of convergence of double rational Fourier series and, in particular, double trigonometric Fourier series of functions of generalized bounded variation is estimated.
About the Authors
R. K. BeraIndia
Rameshbhai Karshanbhai Bera.
Vadodara (Gujarat), 390002
B. L. Ghodadra
India
Bhikha Lila Ghodadra.
Vadodara (Gujarat), 390002
References
1. Bultheel A., Gonzàlez-Vera P., Hendriksen E., Njastad O. Orthogonal rational functions (Cambridge Univ. Press, 1999).
2. Ninness B., Gustafsson F. A unifying construction of orthonormal bases for system identification, IEEE Transact. Automat. Control 42 (4), 515–521 (1997).
3. Vyas R.G. Properties of functions of generalized variation, Math. Anal., Approx. Theory Their Appl. 235 (21), 715–741 (2016).
4. Bojani´c R. An estimate of the rate of convergence for Fourier series of functions of bounded variation, Publ. Inst. Math. (Beograd) (N.S.) 26 (40), 57–60 (1979).
5. Bojani´c R., Waterman D. On the rate of convergence of Fourier series of functions of generalized bounded variation, Akad. Nauka Umjet. Bosne Hercegov. Rad. Odjelj. Prirod. Mat. Nauka 22, 5–11 (1983).
6. Jordan C. Sur la series de Fourier, C. R. Acad. Sci. Paris. 92, 228–230 (1881).
7. Khachar H., Vyas R. Rate of convergence for rational and conjugate rational Fourier series of functions of generalized bounded variation, Acta Comm. Univ. Tartuensis Math. 26 (2), 233–241 (2022).
8. Tan L., Qian T. On convergence of rational Fourier series of functions of bounded variations, Sci. Sin. Math. 43 (6), 541–550 (2013).
9. Wiener N. The quadratic variation of a function and its Fourier coefficients, Mass. J. Math. (3), 72–94 (1924).
10. Бера Р.К., Годадра Б.Л. Скорость сходимости некоторых рядов Фурье функций обобщенной ограниченной вариации, Изв. вузов. Матем. (10), 3–17 (2024).
11. Hardy G.H. On double Fourier series, Quart. J. Math. 35, 53–79 (1906).
12. Moricz F. A quantitative version of the Dirichlet-Jordan test for double Fourier series, J. Approx. Theory 71, 344–358 (1992).
13. Bera R.K., Ghodadra B.L. On the rate of convergence of double Fourier series of functions of generalized bounded variation, Acta Sci. Math. (Szeged) 88, 723–737 (2022).
14. Bera R.K., Ghodadra B.L. Pointwise convergence of the double Fourier-Legendre series of functions of generalized bounded variation, J. Class. Anal. 23 (2), 105–125 (2024).
15. Garnett J.B. Bounded analytic functions (Acad. Press, 1981).
16. Zygmund A. Trigonometric series. V. I (Cambridge Univ. Press, 1959).
Review
For citations:
Bera R.K., Ghodadra B.L. Rate of convergence of double rational Fourier series of functions of generalized bounded variation. Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika. 2025;(5):26-43. (In Russ.) https://doi.org/10.26907/0021-3446-2025-5-26-43