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

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Matematicheskie Zametki, 2011, Volume 90, Issue 3, Pages 362–383
DOI: https://doi.org/10.4213/mzm9224 (Mi mzm9224)

This article is cited in 11 scientific papers (total in 11 papers)

Some Problems of Approximation Theory in the Spaces

L_{p}

$L_p$ on the Line with Power Weight

Iong Ping Li^a, Chun Mei Su^a, V. I. Ivanov^b

^a Beijing Normal University
^b Tula State University

Full-text PDF (604 kB) Citations (11)

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

Abstract: In the spaces

L_{p}

$L_p$ 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

$K$ -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

$K$ -functional.

Keywords: Dunkl difference-differential operator, entire function, Dunkl transform, generalized shift operator, modulus of smoothness, the spaces

L_{p}

$L_p$ , Jackson–Stechkin theorem.

Received: 23.03.2011
Revised: 04.06.2011

English version:
Mathematical Notes, 2011, Volume 90, Issue 3, Pages 344–364
DOI: https://doi.org/10.1134/S0001434611090045

Bibliographic databases:

Document Type: Article

UDC: 517.5

Language: Russian

Citation: Iong Ping Li, Chun Mei Su, V. I. Ivanov, “Some Problems of Approximation Theory in the Spaces

L_{p}

$L_p$ 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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\jour Mat. Zametki

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\issue 3

\pages 362--383

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\crossref{https://doi.org/10.4213/mzm9224}

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\transl

\jour Math. Notes

\yr 2011

\vol 90

\issue 3

\pages 344--364

\crossref{https://doi.org/10.1134/S0001434611090045}

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Linking options:

https://www.mathnet.ru/eng/mzm9224

https://doi.org/10.4213/mzm9224

https://www.mathnet.ru/eng/mzm/v90/i3/p362

This publication is cited in the following 11 articles:

Othman Tyr, “Bernstein's inequalities and Jackson's inverse theorems in the Laguerre hypergroup”, Anal.Math.Phys., 14:2 (2024)
O. L. Vinogradov, “Sharp Bernstein-type inequalities for Fourier-Dunkl multipliers”, Sb. Math., 214:1 (2023), 1–27
O. Tyr, R. Daher, “A note of some approximation theorems of functions on the Laguerre hypergroup”, Filomat, 37:6 (2023), 1959
Daher R., Tyr O., “Modulus of Smoothness and Theorems Concerning Approximation in the Space l-Q,Alpha(2)(R-Q) With Power Weight”, Mediterr. J. Math., 18:2 (2021), 69
Negzaoui S., Oukili S., “Modulus of Continuity and Modulus of Smoothness Related to the Deformed Hankel Transform”, Results Math., 76:3 (2021), 164
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
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
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
S. S. Platonov, “Fourier–Jacobi harmonic analysis and approximation of functions”, Izv. Math., 78:1 (2014), 106–153
Veprintsev R.A., “Nekotorye voprosy garmonicheskogo analiza Danklya na sfere i share”, Izvestiya Tulskogo gosudarstvennogo universiteta. Estestvennye nauki, 2013, no. 3, 6–26
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

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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