منابع مشابه
Dunkl wavelets and applications to inversion of the Dunkl intertwining operator and its dual
These operators are very important inmathematics and physics. They allow the development of generalized wavelets from generalized continuous classical wavelet analysis. Moreover, we have proved in [2] that the generalized two-scale equation associated with the Dunkl operator has a solution and then we can define continuous multiresolution analysis. Dunkl has proved in [1] that there exists a un...
متن کاملInversion Formulas for the Dunkl Intertwining Operator and Its Dual on Spaces of Functions and Distributions⋆
In this paper we prove inversion formulas for the Dunkl intertwining operator Vk and for its dual tVk and we deduce the expression of the representing distributions of the inverse operators V −1 k and V −1 k , and we give some applications.
متن کاملAbsolute continuity of the representing measures of the Dunkl intertwining operator and of its dual and applications
In this paper we prove the absolute continuity of the representing measures of the Dunkl intertwining operator and of its dual. Next we present some applications of this result. Key word : Dunkl intertwining operator and its dual. Absolute continuity of the representing measures. MSC (2000) : 33C80, 51F15, 44A15. Introduction We consider the differential-difference operators on R introduced by ...
متن کاملPositivity of Dunkl’s Intertwining Operator
For a finite reflection group on R , the associated Dunkl operators are parametrized firstorder differential-difference operators which generalize the usual partial derivatives. They generate a commutative algebra which is – under weak assumptions – intertwined with the algebra of partial differential operators by a unique linear and homogeneous isomorphism on polynomials. In this paper it is s...
متن کاملAn Intertwining Operator for the Group B2
There is a commutative algebra of di¤erential-di¤erence operators, acting on polynomials on R2, associated with the reection group B2. This paper presents an integral transform which intertwines this algebra, allowing one free parameter, with the algebra of partial derivatives. The method of proof depends on properties of a certain class of balanced terminating hypergeometric series of 4F3-typ...
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ژورنال
عنوان ژورنال: Journal of Functional Analysis
سال: 2009
ISSN: 0022-1236
DOI: 10.1016/j.jfa.2008.09.018