On the norms of generalized translation operators generated by Dunkl type operators

DOI10.1007/s10958-012-0889-xzbMath1266.47067OpenAlexW2090991655MaRDI QIDQ690818

O. L. Vinogradov

Publication date: 29 November 2012

Published in: Journal of Mathematical Sciences (New York) (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10958-012-0889-x

zbMATH Keywords

integral representationnormsDunkl type operators

Mathematics Subject Classification ID

Special integral transforms (Legendre, Hilbert, etc.) (44A15) Norms (inequalities, more than one norm, etc.) of linear operators (47A30) General theory of ordinary differential operators (47E05) Linear operators on special spaces (weighted shifts, operators on sequence spaces, etc.) (47B37)

Cites Work

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• Convolution structure associated with the Jacobi-Dunkl operator on \(\mathbb R\)
• Product formulas and convolutions for the radial oblate spheroidal wave functions
• Sur un théorème de Paley-Wiener associe à la décomposition spectrale d'un opérateur de Sturm-Liouville sur \([0, \infty\)]
• Convolution operator and maximal function for the Dunkl transform
• The convolution structure for Jacobi function expansions
• Product Formulas and Convolutions for Angular and Radial Spheroidal Wave Functions
• Equiconvergence theorems for Chébli-Trimèche hypergroups
• Differential-Difference Operators Associated to Reflection Groups
• Transmutation operators associated with a dunkl type differential-difference operator on the real line and certain of their applications
• TRANSMUTATION OPERATORS AND PALEY–WIENER THEOREM ASSOCIATED WITH A SINGULAR DIFFERENTIAL-DIFFERENCE OPERATOR ON THE REAL LINE
• A Uniform Expansion for the Eigenfunction of a Singular Second-Order Differential Operator
• A positive radial product formula for the Dunkl kernel

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