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Trudy Inst. Mat. i Mekh. UrO RAN, 2005, Volume 11, Number 2, Pages 72–91 (Mi timm191)  

This article is cited in 14 scientific papers (total in 14 papers)

An integral problem of Konyagin and the $(C,L)$-constants of Nikol'skii

D. V. Gorbachev


Abstract: An extremal problem concerning functions with small supports posed by Konyagin in connection with number-theoretic applications is considered. It is shown to be related to extremal problems on the best Nikol'skii constants in the inequalities for $C$- and $L$-norms of trigonometric polynomials and entire functions of exponential type. New estimates for constants in these problems are obtained.

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English version:
Proceedings of the Steklov Institute of Mathematics (Supplementary issues), 2005, suppl. 2, S117–S138

Bibliographic databases:
UDC: 517.5
Received: 16.07.2004

Citation: D. V. Gorbachev, “An integral problem of Konyagin and the $(C,L)$-constants of Nikol'skii”, Function theory, Trudy Inst. Mat. i Mekh. UrO RAN, 11, no. 2, 2005, 72–91; Proc. Steklov Inst. Math. (Suppl.), 2005no. , suppl. 2, S117–S138

Citation in format AMSBIB
\Bibitem{Gor05}
\by D.~V.~Gorbachev
\paper An integral problem of Konyagin and the $(C,L)$-constants of Nikol'skii
\inbook Function theory
\serial Trudy Inst. Mat. i Mekh. UrO RAN
\yr 2005
\vol 11
\issue 2
\pages 72--91
\mathnet{http://mi.mathnet.ru/timm191}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2200225}
\zmath{https://zbmath.org/?q=an:1126.41016}
\elib{https://elibrary.ru/item.asp?id=12040705}
\transl
\jour Proc. Steklov Inst. Math. (Suppl.)
\yr 2005
\issue , suppl. 2
\pages S117--S138


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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. Benyamini Y., Kroo A., Pinkus A., “L (1)-Approximation and Finding Solutions with Small Support”, Constr. Approx., 36:3 (2012), 399–431  crossref  mathscinet  zmath  isi  elib  scopus
    2. V. V. Arestov, M. V. Deikalova, “Nikol'skii inequality for algebraic polynomials on a multidimensional Euclidean sphere”, Proc. Steklov Inst. Math. (Suppl.), 284, suppl. 1 (2014), 9–23  mathnet  crossref  mathscinet  isi  elib
    3. Yu. V. Malykhin, K. S. Ryutin, “Concentration of the $L_1$-norm of trigonometric polynomials and entire functions”, Sb. Math., 205:11 (2014), 1620–1649  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    4. Arestov V. Deikalova M., “Nikol'Skii Inequality Between the Uniform Norm and l-Q-Norm With Ultraspherical Weight of Algebraic Polynomials on An Interval”, Comput. Methods Funct. Theory, 15:4, SI (2015), 689–708  crossref  mathscinet  zmath  isi  elib  scopus
    5. Ganzburg M.I., Tikhonov S.Yu., “On Sharp Constants in Bernstein-Nikolskii Inequalities”, Constr. Approx., 45:3 (2017), 449–466  crossref  mathscinet  zmath  isi  scopus
    6. Arestov V.V., Deikalova M.V., “Jacobi Translation and the Inequality of Different Metrics For Algebraic Polynomials on An Interval”, Dokl. Math., 95:1 (2017), 21–25  crossref  mathscinet  zmath  isi  scopus
    7. Chunaev P. Danchenko V., “Quadrature Formulas With Variable Nodes and Jackson-Nikolskii Inequalities For Rational Functions”, J. Approx. Theory, 228 (2018), 1–20  crossref  mathscinet  zmath  isi  scopus
    8. 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
    9. D. V. Gorbachev, N. N. Dobrovolskii, “Konstanty Nikolskogo v prostranstvakh $L^{p}(\mathbb{R},|x|^{2\alpha+1} dx)$”, Chebyshevskii sb., 19:2 (2018), 67–79  mathnet  crossref  elib
    10. D. V. Gorbachev, I. A. Martyanov, “O vzaimosvyazi konstant Nikolskogo dlya trigonometricheskikh polinomov i tselykh funktsii eksponentsialnogo tipa”, Chebyshevskii sb., 19:2 (2018), 80–89  mathnet  crossref  elib
    11. Ganzburg I M., “Sharp Constants of Approximation Theory. II. Invariance Theorems and Certain Multivariate Inequalities of Different Metrics”, Constr. Approx., 50:3 (2019), 543–577  crossref  mathscinet  zmath  isi  scopus
    12. Carneiro E., Milinovich M.B., Soundararajan K., “Fourier Optimization and Prime Gaps”, Comment. Math. Helv., 94:3 (2019), 533–568  crossref  mathscinet  zmath  isi  scopus
    13. D. V. Gorbachev, I. A. Martyanov, “Granitsy polinomialnykh konstant Nikolskogo v $L^p$ s vesom Gegenbauera”, Tr. IMM UrO RAN, 26, no. 4, 2020, 126–137  mathnet  crossref  elib
    14. I. A. Martyanov, “Konstanta Nikolskogo dlya trigonometricheskikh polinomov s periodicheskim vesom Gegenbauera”, Chebyshevskii sb., 21:1 (2020), 247–258  mathnet  crossref
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