Research Article
BibTex RIS Cite

Some Approximation Properties of Series with Nonlinear Fourier Basis

Year 2018, , 22 - 27, 31.10.2018
https://doi.org/10.36753/mathenot.476784

Abstract

The order of approximation of generalized de la Vallée Poussin means of series with nonlinear Fourier
basis was investigated in uniform and Hölder norms.

References

  • [1] DeVore, R. A. and Lorentz, G., Constructive Approximation, Springer-Verlag. New York, 1993.
  • [2] Holland, A. S. B., A survey of degree of approximation of continuous functions. SIAM Rev. 23 (1981), 344-379.
  • [3] Huang, C. and Yang L., Approximation by the nonlinear Fourier basis. Sci. China Math. 54 (2011), 1207-1214.
  • [4] Leindler, L., On summability of Fourier series. Acta Sci. Math. Szeged 29 (1968), 147-162.
  • [5] Leindler, L., Meir, A. and Totik, V., On approximation of continuous functions in Lipschitz norms. Acta Math. Hung 45 (1985), 441-443.
  • [6] Prössdorf, S., Zur konvergenz der Fourierreihen hölderstetiger funktionen. Math. Nachr. 69 (1975), 7-14.
  • [7] Qian, T., Analytic signals and harmonic measures. J. Math. Anal. Appl. 314 (2006), 526-536.
  • [8] Qian, T. and Chen, Q., Characterization of analytic phase signals. Comput. Math. Appl. 51 (2006), 1471-1482.
  • [9] Stypinski, Z., On a generalization of the theorem of Prössdorf. Funct. Approx. Comment. Math. 7 (1979), 101-104.
  • [10] Timan, A. F., Theory of approximation of functions of a real variable, Pergamon Press, 1963.
  • [11] Zygmund, A., Trigonometric series, Vols. I-II, 2nd edition, Cambridge Univ. Press, London, 1959.
Year 2018, , 22 - 27, 31.10.2018
https://doi.org/10.36753/mathenot.476784

Abstract

References

  • [1] DeVore, R. A. and Lorentz, G., Constructive Approximation, Springer-Verlag. New York, 1993.
  • [2] Holland, A. S. B., A survey of degree of approximation of continuous functions. SIAM Rev. 23 (1981), 344-379.
  • [3] Huang, C. and Yang L., Approximation by the nonlinear Fourier basis. Sci. China Math. 54 (2011), 1207-1214.
  • [4] Leindler, L., On summability of Fourier series. Acta Sci. Math. Szeged 29 (1968), 147-162.
  • [5] Leindler, L., Meir, A. and Totik, V., On approximation of continuous functions in Lipschitz norms. Acta Math. Hung 45 (1985), 441-443.
  • [6] Prössdorf, S., Zur konvergenz der Fourierreihen hölderstetiger funktionen. Math. Nachr. 69 (1975), 7-14.
  • [7] Qian, T., Analytic signals and harmonic measures. J. Math. Anal. Appl. 314 (2006), 526-536.
  • [8] Qian, T. and Chen, Q., Characterization of analytic phase signals. Comput. Math. Appl. 51 (2006), 1471-1482.
  • [9] Stypinski, Z., On a generalization of the theorem of Prössdorf. Funct. Approx. Comment. Math. 7 (1979), 101-104.
  • [10] Timan, A. F., Theory of approximation of functions of a real variable, Pergamon Press, 1963.
  • [11] Zygmund, A., Trigonometric series, Vols. I-II, 2nd edition, Cambridge Univ. Press, London, 1959.
There are 11 citations in total.

Details

Primary Language English
Journal Section Articles
Authors

Hatice Aslan This is me 0000-0002-3486-4179

Ali Güven 0000-0001-8878-250X

Publication Date October 31, 2018
Submission Date June 6, 2018
Acceptance Date September 13, 2018
Published in Issue Year 2018

Cite

APA Aslan, H., & Güven, A. (2018). Some Approximation Properties of Series with Nonlinear Fourier Basis. Mathematical Sciences and Applications E-Notes, 6(2), 22-27. https://doi.org/10.36753/mathenot.476784
AMA Aslan H, Güven A. Some Approximation Properties of Series with Nonlinear Fourier Basis. Math. Sci. Appl. E-Notes. October 2018;6(2):22-27. doi:10.36753/mathenot.476784
Chicago Aslan, Hatice, and Ali Güven. “Some Approximation Properties of Series With Nonlinear Fourier Basis”. Mathematical Sciences and Applications E-Notes 6, no. 2 (October 2018): 22-27. https://doi.org/10.36753/mathenot.476784.
EndNote Aslan H, Güven A (October 1, 2018) Some Approximation Properties of Series with Nonlinear Fourier Basis. Mathematical Sciences and Applications E-Notes 6 2 22–27.
IEEE H. Aslan and A. Güven, “Some Approximation Properties of Series with Nonlinear Fourier Basis”, Math. Sci. Appl. E-Notes, vol. 6, no. 2, pp. 22–27, 2018, doi: 10.36753/mathenot.476784.
ISNAD Aslan, Hatice - Güven, Ali. “Some Approximation Properties of Series With Nonlinear Fourier Basis”. Mathematical Sciences and Applications E-Notes 6/2 (October 2018), 22-27. https://doi.org/10.36753/mathenot.476784.
JAMA Aslan H, Güven A. Some Approximation Properties of Series with Nonlinear Fourier Basis. Math. Sci. Appl. E-Notes. 2018;6:22–27.
MLA Aslan, Hatice and Ali Güven. “Some Approximation Properties of Series With Nonlinear Fourier Basis”. Mathematical Sciences and Applications E-Notes, vol. 6, no. 2, 2018, pp. 22-27, doi:10.36753/mathenot.476784.
Vancouver Aslan H, Güven A. Some Approximation Properties of Series with Nonlinear Fourier Basis. Math. Sci. Appl. E-Notes. 2018;6(2):22-7.

20477

The published articles in MSAEN are licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.