Symmetries of the $$S_3$$ Dirac–Dunkl Operator

2018 ◽  
pp. 255-260 ◽  
Author(s):  
Hendrik De Bie ◽  
Roy Oste ◽  
Joris Van der Jeugt
Keyword(s):  
Dunkl Operator

Hypercyclic and chaotic convolution operators associated with the Dunkl operator on C

2005 ◽  
Vol 106 (1-2) ◽  
pp. 101-116 ◽  
Author(s):  
J. J. Betancor ◽  
M. Sifi ◽  
K. Triméche
Keyword(s):  
Convolution Operators ◽  
Dunkl Operator

scholarly journals Some Embeddings into the Morrey and Modified Morrey Spaces Associated with the Dunkl Operator

2010 ◽  
Vol 2010 ◽  
pp. 1-10 ◽  
Author(s):  
Emin V. Guliyev ◽  
Yagub Y. Mammadov
Keyword(s):  
Maximal Operator ◽  
Morrey Space ◽  
Shift Operator ◽  
Morrey Spaces ◽  
Dunkl Operator ◽  
Generalized Shift Operator ◽  
Fractional Maximal Operator ◽  
Generalized Shift

We consider the generalized shift operator, associated with the Dunkl operatorΛα(f)(x)=(d/dx)f(x)+((2α+1)/x)((f(x)-f(-x))/2),α>-1/2. We study some embeddings into the Morrey space (D-Morrey space)Lp,λ,α,0≤λ<2α+2and modified Morrey space (modifiedD-Morrey space)L̃p,λ,αassociated with the Dunkl operator onℝ. As applications we get boundedness of the fractional maximal operatorMβ,0≤β<2α+2, associated with the Dunkl operator (fractionalD-maximal operator) from the spacesLp,λ,αtoL∞(ℝ)forp=(2α+2-λ)/βand from the spacesL̃p,λ,α(ℝ)toL∞(ℝ)for(2α+2-λ)/β≤p≤(2α+2)/β.

scholarly journals A higher rank Racah algebra and the $\mathbb{Z}_2^n$ Laplace–Dunkl operator

2017 ◽  
Vol 51 (2) ◽  
pp. 025203 ◽  
Author(s):  
Hendrik De Bie ◽  
Vincent X Genest ◽  
Wouter van de Vijver ◽  
Luc Vinet
Keyword(s):  
Dunkl Operator ◽  
Higher Rank ◽  
Racah Algebra
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