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Zapiski Nauchnykh Seminarov POMI, 2011, Volume 389, Pages 34–57
(Mi znsl4117)
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This article is cited in 5 scientific papers (total in 5 papers)
On the norms of generalized translation operators generated by Jacobi–Dunkl operators
O. L. Vinogradov Saint-Petersburg State University, Saint-Petersburg, Russia
Abstract:
We establish an integral representation and improve the norm estimate for the generalized translation operators generated by Jacobi–Dunkl operators
$$
\Lambda_{\alpha,\beta}f(x)=f'(x)+\frac{A_{\alpha,\beta}'(x)}{A_{\alpha,\beta}(x)}\,\frac{f(x)-f(-x)}2,
$$
where
$$
A_{\alpha,\beta}(x)=(1-\cos x)^\alpha(1+\cos x)^\beta|\sin x|,
$$
in the spaces $L_p[-\pi,\pi]$ with the weight $A_{\alpha,\beta}$. For $\alpha\ge\beta\ge-\frac12$ we prove that these norms do not exceed $2$.
Key words and phrases:
Jacobi polynomials, generalized translation operator, Jacobi–Dunkl operator.
Received: 11.05.2011
Citation:
O. L. Vinogradov, “On the norms of generalized translation operators generated by Jacobi–Dunkl operators”, Investigations on linear operators and function theory. Part 39, Zap. Nauchn. Sem. POMI, 389, POMI, St. Petersburg, 2011, 34–57; J. Math. Sci. (N. Y.), 182:5 (2012), 603–616
Linking options:
https://www.mathnet.ru/eng/znsl4117 https://www.mathnet.ru/eng/znsl/v389/p34
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Abstract page: | 276 | Full-text PDF : | 96 | References: | 34 |
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