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Trudy Inst. Mat. i Mekh. UrO RAN, 2014, Volume 20, Number 1, Pages 109–118 (Mi timm1034)  

This article is cited in 3 scientific papers (total in 3 papers)

Generalized Jackson inequality in the space $L_2(\mathbb R^d)$ with Dunkl weight

V. I. Ivanov, Ha Thi Min Hue

Tula State University

Abstract: A generalized modulus of continuity is defined in the space $L_2(\mathbb R^d)$ with Dunkl weight by means of an arbitrary zero-sum sequence of complex numbers. A sharp generalized Jackson inequality is proved for this modulus and the best approximations by entire functions of exponential spherical type. This inequality was earlier proved by S. N. Vasil'ev in the weightless case.

Keywords: root system, reflection group, Dunkl weight, Dunkl transform, best approximation, modulus of continuity, Jackson inequality.

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English version:
Proceedings of the Steklov Institute of Mathematics (Supplementary issues), 2015, 288, suppl. 1, 88–98

Bibliographic databases:

Document Type: Article
UDC: 517.5
Received: 10.12.2013

Citation: V. I. Ivanov, Ha Thi Min Hue, “Generalized Jackson inequality in the space $L_2(\mathbb R^d)$ with Dunkl weight”, Trudy Inst. Mat. i Mekh. UrO RAN, 20, no. 1, 2014, 109–118; Proc. Steklov Inst. Math. (Suppl.), 288, suppl. 1 (2015), 88–98

Citation in format AMSBIB
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\paper Generalized Jackson inequality in the space $L_2(\mathbb R^d)$ with Dunkl weight
\serial Trudy Inst. Mat. i Mekh. UrO RAN
\yr 2014
\vol 20
\issue 1
\pages 109--118
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\jour Proc. Steklov Inst. Math. (Suppl.)
\yr 2015
\vol 288
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\pages 88--98
\crossref{https://doi.org/10.1134/S0081543815020108}
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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. V. I. Ivanov, A. V. Ivanov, “Optimal Arguments in the Jackson–Stechkin Inequality in $L_2(\mathbb{R}^d)$ with Dunkl Weight”, Math. Notes, 96:5 (2014), 666–677  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    2. D. V. Gorbachev, V. I. Ivanov, S. Yu. Tikhonov, “Pitt's Inequalities and Uncertainty Principle For Generalized Fourier Transform”, Int. Math. Res. Notices, 2016, no. 23, 7179–7200  crossref  mathscinet  isi  scopus
    3. S. B. Vakarchuk, “Best Polynomial Approximations and Widths of Classes of Functions in the Space $L_2$”, Math. Notes, 103:2 (2018), 308–312  mathnet  crossref  crossref  isi  elib
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