Complex Dunkl operators
Guangbin Ren, Helmuth R. Malonek
TL;DR
This paper introduces complex Dunkl operators for certain Coxeter groups, extending the real Dunkl theory into the complex domain and enabling complex analysis of these operators.
Contribution
The paper develops the theory of complex Dunkl operators for specific Coxeter groups, establishing their commutative property and opening new avenues for complex Dunkl analysis.
Findings
Complex Dunkl operators are introduced for certain Coxeter groups.
These operators are shown to be commutative.
The work enables the development of complex Dunkl analysis.
Abstract
The real theory of the Dunkl operators has been developed very extensively, while there still lacks the corresponding complex theory. In this paper we introduce the complex Dunkl operators for certain Coxeter groups. These complex Dunkl operators have the commutative property, which makes it possible to establish a corresponding complex analysis of Dunkl operators.
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Taxonomy
TopicsMathematical Analysis and Transform Methods · Algebraic and Geometric Analysis · Spectral Theory in Mathematical Physics