A. Yu. Trynin, “A criterion for the uniform convergence of sinc-approximations on a segment”, Izv. Vyssh. Uchebn. Zaved. Mat., 2008, no. 6, 66–78; Russian Math. (Iz. VUZ), 52:6 (2008), 58

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Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2008, Number 6, Pages 66–78 (Mi ivm1514)

This article is cited in 24 scientific papers (total in 24 papers)

A criterion for the uniform convergence of sinc-approximations on a segment

A. Yu. Trynin

Saratov State University

Full-text PDF (223 kB) Citations (24)

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Abstract: In this paper we obtain a criterion for the uniform convergence inside the interval

$(0,\pi)$ of values of E. T. Whittaker operators

$L_n(f,x)=\sum_{k=0}^{n}\frac{\sin(nx-k\pi)}{nx-k\pi}f\biggl(\frac{k\pi}{n}\biggr)$
for continuous functions. This criterion is similar to that of A. A. Privalov for the convergence of interpolation Lagrange–Chebyshev polynomials and trigonometric ones.

Keywords: cardinal function, sinc approximation, Lagrange interpolation, convergence; criterion of the uniform convergence, cardinal function, approximation, interpolation process.

Received: 13.02.2006

English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2008, Volume 52, Issue 6, Pages 58–69
DOI: https://doi.org/10.3103/S1066369X08060078

Bibliographic databases:

UDC: 517.518

Language: Russian

Citation: A. Yu. Trynin, “A criterion for the uniform convergence of sinc-approximations on a segment”, Izv. Vyssh. Uchebn. Zaved. Mat., 2008, no. 6, 66–78; Russian Math. (Iz. VUZ), 52:6 (2008), 58–69

Citation in format AMSBIB

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This publication is cited in the following 24 articles:

V. N. Pasechnik, “Approximation of Continuous Functions by Classical Sincs and Values of Operators Cλ”, Comput. Math. and Math. Phys., 64:2 (2024), 206
A. Yu. Trynin, “On a method for solving a mixed boundary value problem for a parabolic equation using modified sinc-approximation operators”, Comput. Math. Math. Phys., 63:7 (2023), 1264–1284
A. Yu. Trynin, “A Summation Method for Trigonometric Fourier Series Based on Sinc-Approximations”, J Math Sci, 270:6 (2023), 842
A. Yu. Trynin, “Lagrange–Sturm–Liouville Processes”, J Math Sci, 261:3 (2022), 455
A. Yu. Trynin, “Sufficient Conditions for Convergence of Generalized Sinc-Approximations on Segment”, J Math Sci, 255:4 (2021), 513
A. Yu. Trynin, “On the uniform approximation of functions of bounded variation by Lagrange interpolation polynomials with a matrix ${\mathcal L}_n^{(\alpha_n,\beta_n)}$ of Jacobi nodes”, Izv. Math., 84:6 (2020), 1224–1249
A. Yu. Trynin, “Error Estimate for Uniform Approximation by Lagrange–Sturm–Liouville Processes”, J Math Sci, 247:6 (2020), 939
A. Yu. Trynin, “Uniform convergence of Lagrange–Sturm–Liouville processes on one functional class”, Ufa Math. J., 10:2 (2018), 93–108
A. Yu. Trynin, “Skhodimost protsessov Lagranzha–Shturma–Liuvillya dlya nepreryvnykh funktsii ogranichennoi variatsii”, Vladikavk. matem. zhurn., 20:4 (2018), 76–91
A. Yu. Trynin, “Sufficient condition for convergence of Lagrange–Sturm–Liouville processes in terms of one-sided modulus of continuity”, Comput. Math. Math. Phys., 58:11 (2018), 1716–1727
Mohsen A.A.K., “Accurate Function Sinc Interpolation and Derivative Estimations Over Finite Intervals”, J. Comput. Appl. Math., 324 (2017), 216–224
Coroianu L., Gal S.G., “L-P-Approximation By Truncated Max-Product Sampling Operators of Kantorovich-Type Based on Fejer Kernel”, J. Integral Equ. Appl., 29:2 (2017), 349–364
A. Yu. Trynin, “Approximation of continuous on a segment functions with the help of linear combinations of sincs”, Russian Math. (Iz. VUZ), 60:3 (2016), 63–71
Coroianu L., Gal S.G., “Localization Results For the Non-Truncated Max-Product Sampling Operators Based on Fejer and Sinc-Type Kernels”, Demonstr. Math., 49:1 (2016), 38–49
A. Yu. Trynin, “Neobkhodimye i dostatochnye usloviya ravnomernoi na otrezke sink-approksimatsii funktsii ogranichennoi variatsii”, Izv. Sarat. un-ta. Nov. ser. Ser.: Matematika. Mekhanika. Informatika, 16:3 (2016), 288–298
A. Ya. Umakhanov, I. I. Sharapudinov, “Interpolyatsiya funktsii summami Uittekera i ikh modifikatsiyami: usloviya ravnomernoi skhodimosti”, Vladikavk. matem. zhurn., 18:4 (2016), 61–70
A. Yu. Trynin, “On necessary and sufficient conditions for convergence of sinc-approximations”, St. Petersburg Math. J., 27:5 (2016), 825–840
A. Yu. Trynin, “On some properties of sinc approximations of continuous functions on the interval”, Ufa Math. J., 7:4 (2015), 111–126
Lucian Coroianu, Sorin G. Gal, “Saturation Results for the Truncated Max-Product Sampling Operators Based on Sinc and Fejér-Type Kernels”, STSIP, 11:1 (2012), 113
A. Yu. Trynin, “On operators of interpolation with respect to solutions of a Cauchy problem and Lagrange–Jacobi polynomials”, Izv. Math., 75:6 (2011), 1215–1248

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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