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Mat. Sb., 2015, Volume 206, Number 8, Pages 63–98 (Mi msb8413)  

This article is cited in 9 scientific papers (total in 9 papers)

Gauss and Markov quadrature formulae with nodes at zeros of eigenfunctions of a Sturm-Liouville problem, which are exact for entire functions of exponential type

D. V. Gorbachev, V. I. Ivanov

Tula State University

Abstract: Gauss and Markov quadrature formulae with nodes at zeros of eigenfunctions of a Sturm-Liouville problem, which are exact for entire functions of exponential type, are established. They generalize quadrature formulae involving zeros of Bessel functions, which were first designed by Frappier and Olivier. Bessel quadratures correspond to the Fourier-Hankel integral transform. Some other examples, connected with the Jacobi integral transform, Fourier series in Jacobi orthogonal polynomials and the general Sturm-Liouville problem with regular weight are also given.
Bibliography: 39 titles.

Keywords: Gauss and Markov quadrature formulae, entire function of exponential type, Sturm-Liouville problem, Jacobi transform, Jacobi functions and polynomials.

Funding Agency Grant Number
Russian Foundation for Basic Research 13-01-00045
Ministry of Education and Science of the Russian Federation 5414ГЗ
1.1333.2014К
Dynasty Foundation
This research was carried out with the support of the Russian Foundation for Basic Research (grant no. 13-01-00045), the Ministry of Education and Science of the Russian Federation (state contract nos. 5414ГЗ and~1.1333.2014K) and D. Zimin's "Dynasty" foundation.

Author to whom correspondence should be addressed

DOI: https://doi.org/10.4213/sm8413

Full text: PDF file (697 kB)
References: PDF file   HTML file

English version:
Sbornik: Mathematics, 2015, 206:8, 1087–1122

Bibliographic databases:

UDC: 517.518.87
MSC: Primary 41A55; Secondary 30D15, 34B25
Received: 31.07.2014 and 14.11.2014

Citation: D. V. Gorbachev, V. I. Ivanov, “Gauss and Markov quadrature formulae with nodes at zeros of eigenfunctions of a Sturm-Liouville problem, which are exact for entire functions of exponential type”, Mat. Sb., 206:8 (2015), 63–98; Sb. Math., 206:8 (2015), 1087–1122

Citation in format AMSBIB
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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. D. V. Gorbachev, V. I. Ivanov, “Approximation in $L_2$ by Partial Integrals of the Fourier Transform over the Eigenfunctions of the Sturm–Liouville Operator”, Math. Notes, 100:4 (2016), 540–549  mathnet  crossref  crossref  mathscinet  isi  elib
    2. D. V. Gorbachev, V. I. Ivanov, “Bohman extremal problem for the Jacobi transform”, Proc. Steklov Inst. Math. (Suppl.), 300, suppl. 1 (2018), 88–96  mathnet  crossref  crossref  mathscinet  isi  elib
    3. D. V. Gorbachev, V. I. Ivanov, R. A. Veprintsev, “Approximation in $L_2$ by partial integrals of the multidimensional Fourier transform in the eigenfunctions of the Sturm–Liouville operator”, Proc. Steklov Inst. Math. (Suppl.), 300, suppl. 1 (2018), 97–113  mathnet  crossref  crossref  mathscinet  isi  elib
    4. D. V. Gorbachev, V. I. Ivanov, “Nekotorye ekstremalnye zadachi dlya preobrazovaniya Fure po sobstvennym funktsiyam operatora Shturma–Liuvillya”, Chebyshevskii sb., 18:2 (2017), 34–53  mathnet  crossref  elib
    5. D. V. Gorbachev, V. I. Ivanov, E. P. Ofitserov, O. I. Smirnov, “Nekotorye ekstremalnye zadachi garmonicheskogo analiza i teorii priblizhenii”, Chebyshevskii sb., 18:4 (2017), 140–167  mathnet  crossref
    6. D. V. Gorbachev, “Konstanty Nikolskogo - Bernshteina dlya neotritsatelnykh tselykh funktsii eksponentsialnogo tipa na osi”, Tr. IMM UrO RAN, 24, no. 4, 2018, 92–103  mathnet  crossref  elib
    7. D. V. Gorbachev, V. I. Ivanov, “Turan's and Fejer's extremal problems for Jacobi transform”, Anal. Math., 44:4 (2018), 419–432  crossref  mathscinet  zmath  isi
    8. D. V. Gorbachev, V. I. Ivanov, E. P. Ofitserov, O. I. Smirnov, “Vtoraya ekstremalnaya zadacha Logana dlya preobrazovaniya Fure po sobstvennym funktsiyam operatora Shturma–Liuvillya”, Chebyshevskii sb., 19:1 (2018), 57–78  mathnet  crossref  elib
    9. D. V. Gorbachev, V. I. Ivanov, “Turán, Fejér and Bohman extremal problems for the multivariate Fourier transform in terms of the eigenfunctions of a Sturm-Liouville problem”, Sb. Math., 210:6 (2019), 809–835  mathnet  crossref  crossref  adsnasa  isi  elib
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