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

Jorge Bustamante

doi:10.33205/cma.1063594

Research Article

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

Year 2022, , 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

Thanks

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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, , 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

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.