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Mat. Zametki, 2016, Volume 100, Issue 4, Pages 519–530 (Mi mz11110)  

This article is cited in 5 scientific papers (total in 5 papers)

Approximation in $L_2$ by Partial Integrals of the Fourier Transform over the Eigenfunctions of the Sturm–Liouville Operator

D. V. Gorbachev, V. I. Ivanov

Tula State University

Abstract: For approximations in the space $L_2(\mathbb{R}_+)$ by partial integrals of the Fourier transform over the eigenfunctions of the Sturm–Liouville operator, we prove Jackson's inequality with exact constant and optimal argument in the modulus of continuity. The optimality of the argument in the modulus of continuity is established using the Gauss quadrature formula on the half-line over the zeros of the eigenfunction of the Sturm–Liouville operator.

Keywords: Sturm–Liouville operator on the half-line, the space $L_2$, Fourier transform, Jackson's inequality, Gauss quadrature formula.

Funding Agency Grant Number
Russian Foundation for Basic Research 16-01-00308
Ministry of Education and Science of the Russian Federation 5414ГЗ
1.1333.2014К
Dynasty Foundation
This work was supported by the Ministry of Education and Science of the Russian Federation (grant no. 5414GZ and no. 1.1333.2014K), by the Russian Foundation for Basic Research under grant 16-01-00308, and the “Dynasty” Foundation of D. Zimin.


DOI: https://doi.org/10.4213/mzm11110

Full text: PDF file (537 kB)
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English version:
Mathematical Notes, 2016, 100:4, 540–549

Bibliographic databases:

UDC: 517.5
Received: 09.02.2016

Citation: 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”, Mat. Zametki, 100:4 (2016), 519–530; Math. Notes, 100:4 (2016), 540–549

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. 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
    2. 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
    3. 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
    4. 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
    5. V. I. Ivanov, D. V. Gorbachev, O. I. Smirnov, E. P. Ofitserov, “Vtoraya ekstremalnaya zadacha Logana dlya preobrazovaniya Fure po sobstvennym funktsiyam operatora Shturma–Liuvillya”, Chebyshevskii sb., 19:1 (2018), 57–78  mathnet  crossref  elib
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