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Mat. Zametki, 2011, Volume 90, Issue 3, Pages 362–383 (Mi mz9224)  

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

Some Problems of Approximation Theory in the Spaces $L_p$ on the Line with Power Weight

Iong Ping Lia, Chun Mei Sua, V. I. Ivanovb

a Beijing Normal University
b Tula State University

Abstract: In the spaces $L_p$ on the line with power weight, we study approximation of functions by entire functions of exponential type. Using the Dunkl difference-differential operator and the Dunkl transform, we define the generalized shift operator, the modulus of smoothness, and the $K$-functional. We prove a direct and an inverse theorem of Jackson–Stechkin type and of Bernstein type. We establish the equivalence between the modulus of smoothness and the $K$-functional.

Keywords: Dunkl difference-differential operator, entire function, Dunkl transform, generalized shift operator, modulus of smoothness, the spaces $L_p$, Jackson–Stechkin theorem

DOI: https://doi.org/10.4213/mzm9224

Full text: PDF file (604 kB)
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English version:
Mathematical Notes, 2011, 90:3, 344–364

Bibliographic databases:

UDC: 517.5
Received: 23.03.2011
Revised: 04.06.2011

Citation: Iong Ping Li, Chun Mei Su, V. I. Ivanov, “Some Problems of Approximation Theory in the Spaces $L_p$ on the Line with Power Weight”, Mat. Zametki, 90:3 (2011), 362–383; Math. Notes, 90:3 (2011), 344–364

Citation in format AMSBIB
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\by Iong Ping Li, Chun Mei Su, V.~I.~Ivanov
\paper Some Problems of Approximation Theory in the Spaces~$L_p$ on the Line with Power Weight
\jour Mat. Zametki
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\vol 90
\issue 3
\pages 362--383
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\crossref{https://doi.org/10.4213/mzm9224}
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\transl
\jour Math. Notes
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\pages 344--364
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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. Ivanov V.I., Lyu Yunpin, Smirnov O.I., “O nekotorykh klassakh tselykh funktsii eksponentsialnogo tipa v prostranstvakh $L_p(\mathbb{R}^d)$ so stepennym vesom”, Izvestiya Tulskogo gosudarstvennogo universiteta. Seriya: Estestvennye nauki, 2011, no. 2, 70–80  mathscinet  elib
    2. Veprintsev R.A., “Nekotorye voprosy garmonicheskogo analiza Danklya na sfere i share”, Izvestiya Tulskogo gosudarstvennogo universiteta. Estestvennye nauki, 2013, no. 3, 6–26  elib
    3. S. S. Platonov, “Fourier–Jacobi harmonic analysis and approximation of functions”, Izv. Math., 78:1 (2014), 106–153  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    4. Daher R., El Ouadih S., “On the Approximation By Entire Functions of Exponential Type in l (P,Alpha) (R)”, J. Pseudo-Differ. Oper. Appl., 8:2 (2017), 341–347  crossref  mathscinet  zmath  isi  scopus
    5. Gorbachev D.V. Ivanov V.I. Tikhonov S.Yu., “Positive l-P-Bounded Dunkl-Type Generalized Translation Operator and Its Applications”, Constr. Approx., 49:3 (2019), 555–605  crossref  isi
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