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Izv. RAN. Ser. Mat., 2011, Volume 75, Issue 6, Pages 129–162 (Mi izv4275)  

This article is cited in 7 scientific papers (total in 7 papers)

On operators of interpolation with respect to solutions of a Cauchy problem and Lagrange–Jacobi polynomials

A. Yu. Trynin

Saratov State University named after N. G. Chernyshevsky

Abstract: We describe classes of continuous functions for which one has pointwise and uniform convergence of certain Lagrange-type operators (constructed from solutions of a Cauchy problem) and the Lagrange–Jacobi interpolation polynomials ${\mathcal L}_n^{(\alpha_{n},\beta_{n})}(F,\cos\theta)$. We also obtain sufficient conditions for the equiconvergence of these interpolation processes.

Keywords: interpolation processes, Lagrange operators, sampling theorem, theory of approximation of functions.

DOI: https://doi.org/10.4213/im4275

Full text: PDF file (730 kB)
References: PDF file   HTML file

English version:
Izvestiya: Mathematics, 2011, 75:6, 1215–1248

Bibliographic databases:

UDC: 517.518.85
MSC: 41A05, 41A35, 34B24
Received: 14.12.2009
Revised: 21.11.2010

Citation: A. Yu. Trynin, “On operators of interpolation with respect to solutions of a Cauchy problem and Lagrange–Jacobi polynomials”, Izv. RAN. Ser. Mat., 75:6 (2011), 129–162; Izv. Math., 75:6 (2011), 1215–1248

Citation in format AMSBIB
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  • https://doi.org/10.4213/im4275
  • http://mi.mathnet.ru/eng/izv/v75/i6/p129

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

    This publication is cited in the following articles:
    1. A. Yu. Trynin, “On necessary and sufficient conditions for convergence of sinc-approximations”, St. Petersburg Math. J., 27:5 (2016), 825–840  mathnet  crossref  mathscinet  isi  elib
    2. A. Yu. Trynin, “On some properties of sinc approximations of continuous functions on the interval”, Ufa Math. J., 7:4 (2015), 111–126  mathnet  crossref  isi  elib
    3. 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  mathnet  crossref  isi
    4. 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  mathnet  crossref  mathscinet  elib
    5. A. Yu. Trynin, “Uniform convergence of Lagrange–Sturm–Liouville processes on one functional class”, Ufa Math. J., 10:2 (2018), 93–108  mathnet  crossref  isi
    6. A. Yu. Trynin, “Skhodimost protsessov Lagranzha–Shturma–Liuvillya dlya nepreryvnykh funktsii ogranichennoi variatsii”, Vladikavk. matem. zhurn., 20:4 (2018), 76–91  mathnet  crossref
    7. 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  mathnet  crossref  crossref  isi  elib
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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