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Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2014, Volume 20, Number 1, Pages 109–118 (Mi timm1034)  
This article is cited in 4 scientific papers (total in 4 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
Full-text PDF (182 kB) Citations (4)
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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.
Received: 10.12.2013
English version:
Proceedings of the Steklov Institute of Mathematics (Supplementary issues), 2015, Volume 288, Issue 1, Pages 88–98
DOI: https://doi.org/10.1134/S0081543815020108
Bibliographic databases:
Document Type: Article
UDC: 517.5
Language: Russian
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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  • https://www.mathnet.ru/eng/timm1034
  • https://www.mathnet.ru/eng/timm/v20/i1/p109
    • This publication is cited in the following 4 articles:
    1. S. B. Vakarchuk, “On Estimates in $L_2(\mathbb{R})$ of Mean $\nu$-Widths of Classes of Functions Defined via the Generalized Modulus of Continuity of $\omega_{\mathcal{M}}$”, Math. Notes, 106:2 (2019), 191–202  mathnet  crossref  crossref  mathscinet  isi  elib
    2. 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  mathscinet  isi  elib
    3. 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
    4. 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
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Trudy Instituta Matematiki i Mekhaniki UrO RAN
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    Abstract page:826
    Full-text PDF :122
    References:101
    First page:27
     
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