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Power of Dirichlet kernels and approximation by discrete linear operators $\textit{I}$: direct results

Year 2022, Volume: 5 Issue: 2, 105 - 118, 15.06.2022

Jorge Bustamante

https://doi.org/10.33205/cma.1063594

Abstract

The second and third powers of the Dirichlet kernel are used to construct discrete linear operators for the approximation of continuous periodic functions. An estimate of the rate of convergence is given. Approximation of non-periodic functions are also considered.

Keywords

Discrete linear operators rate of convergence direct results Dirichlet kernel

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References

  • R. Bojanic, O. Shisha: Approximation of continuous, periodic functions by discrete linear positive operators, J. Approximation Theory, 11 (1974), 231–235.
  • J. Bustamante, L. Flores-de-Jesús: Strong converse inequalities and quantitative Voronovskaya-type theorems for trigonometric Fejér sums, Constr. Math. Anal., 3 (2) (2020), 53-63.
  • P. L. Butzer, R. J. Nessel: Fourier Analysis and Approximation, Academic Press, New-York and London, (1971).
  • P. L. Butzer, R. J. Stens: Chebyshev transform methods in the theory of best algebraic approximation, Abh. Math. Sem. Univ. Hamburg, 45 (1976), 165-190.
  • R. DeVore: The Approximation of Continuous Functions by Positive Linear Operators, Lecture Notes in Mathematics No. 293, Springer-Verlag Berlin / Heidelberg / New York, (1972).
  • S. Foucart, Y. Kryakin and A. Shadrin: On the exact constant in the Jackson-Stechkin inequality for the uniform metric, Constr. Approx., 29 (2009), 157-179.
  • R. B. Saxena, K. B. Srivastava: On interpolation operators (I), Anal. Numér. Théor. Approx., 7 (2) (1978), 211-223.
  • S. B. Stechkin: Order of best approximation of continuous functions (in Russian), Izv. Akad. Nauk SSSR, 15 (3) (1951), 219-242.
  • O. Kis, P. Vértesi: On a new interpolation process (in Russian), Ann. Univ. Sci. Budapest. Eötvös Sect. Math., 10 (1967), 117-128.

Year 2022, Volume: 5 Issue: 2, 105 - 118, 15.06.2022

Jorge Bustamante

https://doi.org/10.33205/cma.1063594

Abstract

References

  • R. Bojanic, O. Shisha: Approximation of continuous, periodic functions by discrete linear positive operators, J. Approximation Theory, 11 (1974), 231–235.
  • J. Bustamante, L. Flores-de-Jesús: Strong converse inequalities and quantitative Voronovskaya-type theorems for trigonometric Fejér sums, Constr. Math. Anal., 3 (2) (2020), 53-63.
  • P. L. Butzer, R. J. Nessel: Fourier Analysis and Approximation, Academic Press, New-York and London, (1971).
  • P. L. Butzer, R. J. Stens: Chebyshev transform methods in the theory of best algebraic approximation, Abh. Math. Sem. Univ. Hamburg, 45 (1976), 165-190.
  • R. DeVore: The Approximation of Continuous Functions by Positive Linear Operators, Lecture Notes in Mathematics No. 293, Springer-Verlag Berlin / Heidelberg / New York, (1972).
  • S. Foucart, Y. Kryakin and A. Shadrin: On the exact constant in the Jackson-Stechkin inequality for the uniform metric, Constr. Approx., 29 (2009), 157-179.
  • R. B. Saxena, K. B. Srivastava: On interpolation operators (I), Anal. Numér. Théor. Approx., 7 (2) (1978), 211-223.
  • S. B. Stechkin: Order of best approximation of continuous functions (in Russian), Izv. Akad. Nauk SSSR, 15 (3) (1951), 219-242.
  • O. Kis, P. Vértesi: On a new interpolation process (in Russian), Ann. Univ. Sci. Budapest. Eötvös Sect. Math., 10 (1967), 117-128.
There are 9 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

Jorge Bustamante 0000-0003-2856-6738

Publication Date June 15, 2022
Published in Issue Year 2022 Volume: 5 Issue: 2

Cite

APA Bustamante, J. (2022). Power of Dirichlet kernels and approximation by discrete linear operators $\textit{I}$: direct results. Constructive Mathematical Analysis, 5(2), 105-118. https://doi.org/10.33205/cma.1063594
AMA Bustamante J. Power of Dirichlet kernels and approximation by discrete linear operators $\textit{I}$: direct results. CMA. June 2022;5(2):105-118. doi:10.33205/cma.1063594
Chicago Bustamante, Jorge. “Power of Dirichlet Kernels and Approximation by Discrete Linear Operators $\textit{I}$: Direct Results”. Constructive Mathematical Analysis 5, no. 2 (June 2022): 105-18. https://doi.org/10.33205/cma.1063594.
EndNote Bustamante J (June 1, 2022) Power of Dirichlet kernels and approximation by discrete linear operators $\textit{I}$: direct results. Constructive Mathematical Analysis 5 2 105–118.
IEEE J. Bustamante, “Power of Dirichlet kernels and approximation by discrete linear operators $\textit{I}$: direct results”, CMA, vol. 5, no. 2, pp. 105–118, 2022, doi: 10.33205/cma.1063594.
ISNAD Bustamante, Jorge. “Power of Dirichlet Kernels and Approximation by Discrete Linear Operators $\textit{I}$: Direct Results”. Constructive Mathematical Analysis 5/2 (June 2022), 105-118. https://doi.org/10.33205/cma.1063594.
JAMA Bustamante J. Power of Dirichlet kernels and approximation by discrete linear operators $\textit{I}$: direct results. CMA. 2022;5:105–118.
MLA Bustamante, Jorge. “Power of Dirichlet Kernels and Approximation by Discrete Linear Operators $\textit{I}$: Direct Results”. Constructive Mathematical Analysis, vol. 5, no. 2, 2022, pp. 105-18, doi:10.33205/cma.1063594.
Vancouver Bustamante J. Power of Dirichlet kernels and approximation by discrete linear operators $\textit{I}$: direct results. CMA. 2022;5(2):105-18.
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