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OL Vinogradov (2011)
On the norms of generalized translation operators generated by Jacobi-Dunkl operatorsZap. Nauchn. Sem. POMI, 389
P. Túrán (1975)
On orthogonal polynomialsAnalysis Mathematica, 1
H. Bavinck (1971)
Approximation processes for fourier-jacobi expansions †Applicable Analysis, 5
A. Timan (1994)
Theory of Approximation of Functions of a Real Variable
(1948)
A generalization of an inequality of S
J. Löfström, J. Peetre (1969)
Approximation theorems connected with generalized translationsMathematische Annalen, 181
O. Tyr, R. Daher (2022)
Abilov’s estimates for the Clifford–Fourier transform in real Clifford algebras analysisANNALI DELL'UNIVERSITA' DI FERRARA, 69
R. Daher, O. Tyr (2021)
Modulus of Smoothness and Theorems Concerning Approximation in the Space L 2 q,α ( R q ) with Power Weight
S. Platonov (2009)
Some problems in the theory of approximation of functions on compact homogeneous manifoldsSbornik Mathematics, 200
R. Daher, O. Tyr (2020)
Weighted approximation for the generalized discrete Fourier–Jacobi transform on space $$L_{p}({\mathbb {T}})$$Journal of Pseudo-differential Operators and Applications, 11
O. Vinogradov (2012)
On the norms of generalized translation operators generated by the jacobi-dunkl operatorsJournal of Mathematical Sciences, 182
ES Belkina (2008)
315Izv. Vyssh. Uchebn. Zaved. Mat., 8
G. Gasper (1971)
Positivity and the Convolution Structure for Jacobi SeriesAnnals of Mathematics, 93
AN Tikhonov, AA Samarskii (1964)
10.1063/1.3051872Equations of Mathematical Physics
Сергей Платонов, S. Platonov (2014)
Fourier–Jacobi harmonic analysis and approximation of functionsIzvestiya: Mathematics, 78
O. Vinogradov (2012)
Estimates of functionals by deviations of Steklov type averages generated by Dunkl type operatorsJournal of Mathematical Sciences, 184
R. Daher, O. Tyr (2020)
Equivalence of K-functionals and modulus of smoothness generated by a generalized Jacobi–Dunkl transform on the real lineRendiconti del Circolo Matematico di Palermo Series 2, 70
Feng Dai (2003)
Some equivalence theorems with K-functionalsJ. Approx. Theory, 121
R. Askey, S. Wainger (1969)
A CONVOLUTION STRUCTURE FOR JACOBI SERIES.American Journal of Mathematics, 91
Weighted approximation for the generalized discrete Fourier–Jacobi transform on space L p ( T )
R. Daher, O. Tyr (2021)
Modulus of Smoothness and Theorems Concerning Approximation in the Space $$L^{2}_{q,\alpha }(\mathbb {R}_{q})$$ L qMediterranean Journal of Mathematics, 18
E. Belkina, S. Platonov (2008)
Equivalence of K-functionals and modulus of smoothness constructed by generalized Dunkl translationsRussian Mathematics, 52
O Tyr, R Daher, S El Ouadih, O El Fourchi (2021)
On the Jackson-type inequalities in approximation theory connected to the q\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ q $$\end{document}-Dunkl operators in the weighted space Lq,α2(Rq,|x|2α+1dqx)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L^{2}_{q,\alpha }(\mathbb{R} _{q},|x|^{2\alpha +1}d_{q}x)$$\end{document}Bol. Soc. Mat. Mex., 27
O. Vinogradov (2012)
Estimates of functionals by generalized moduli of continuity generated by the dunkl operatorsJournal of Mathematical Sciences, 184
Christina Kluge (2016)
Semi Groups Of Operators And Approximation
Dunham Jackson
Über die Genauigkeit der Annäherung stetiger Funktionen durch ganze rationale Funktionen gegebenen Grades und trigonometrische Summen gegebener Ordnung
S. ouadih, R. Daher, O. Tyr, Faouaz Saadi (2021)
Equivalence of K-functionals and moduli of smoothness generated by the Beltrami-Laplace operator on the spaces S(p,q)(σm-1)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek}Rendiconti del Circolo Matematico di Palermo Series 2, 71
V. Vladimirov (1972)
Equations of mathematical physics
S. Nikol, I. Ski (1975)
Approximation of Functions of Several Variables and Imbedding Theorems
F. Chouchene (2014)
Bounds, Asymptotic Behavior and Recurrence Relations for the Jacobi-Dunkl Polynomials, 6
Z. Ditzian, V. Totik (1987)
Moduli of smoothness
K. Stempak (2023)
Harmonic Analysis Associated with the Jacobi–Dunkl Operator on $$(-\pi ,\pi )$$ ( - π , π )Complex Analysis and Operator Theory, 17
(1952)
On the best approximation of continuous functions by polynomials of given degree, 1912
S. Ouadih, R. Daher, O. Tyr, Faouaz Saadi (2021)
Equivalence of K-functionals and moduli of smoothness generated by the Beltrami-Laplace operator on the spaces $$S^{(p,q)}(\sigma ^{m-1})$$ SRendiconti del Circolo Matematico di Palermo Series 2, 71
F. Chouchene (2005)
Harmonic analysis associated with the Jacobi-Dunkl operator on ]-π/2, π/2[Journal of Computational and Applied Mathematics, 178
(1968)
A Theory of Interpolation of Normed Spaces
ES Belkina, SS Platonov (2008)
Equivalence of K-functionals and modulus of smoothness constructed by generalized dunkl translationsIzv. Vyssh. Uchebn. Zaved. Mat., 8
On the Jackson - type inequalities in approximation theory connected to the q - Dunkl operators in the weighted space L 2 q , α ( R q , | x | 2 α + 1 d q x )
This paper uses some basic notions and results from the discrete harmonic analysis associated with the Jacobi–Dunkl operator to study some problems in the theory of approximation of functions in the space L2(α,β)\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$ \mathbb {L}_{2}^{(\alpha ,\beta )} $$\end{document}. Analogs of the direct Jackson theorems of approximations for the modulus of smoothness (of arbitrary order) constructed using the translation operators which was defined by Vinogradov are proved. In conclusion of this work, we show that the modulus of smoothness and the K-functionals constructed from the Sobolev-type space corresponding to the Jacobi–Dunkl Laplacian operator are equivalent.
Mediterranean Journal of Mathematics – Springer Journals
Published: Oct 1, 2022
Keywords: Jacobi–Dunkl operator; Jacobi polynomials; discrete Jacobi–Dunkl transform; Jacobi–Dunkl translation operator; Jacobi–Dunkl Laplacian operator; K-functionals; modulus of smoothness; 41A36; 44A20; 42C05; 33C45
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