On the fractional Dunkl Laplacian
F. Bouzeffour, W. Jedidi
TL;DR
This paper develops a framework for the fractional Dunkl Laplacian, providing pointwise formulas, Bochner subordination, and an extension problem, advancing the understanding of fractional operators with reflection symmetries.
Contribution
It introduces a novel approach to the fractional Dunkl Laplacian, including explicit formulas and extension techniques, expanding the mathematical toolkit for reflection-symmetric operators.
Findings
Derived pointwise formulas for the fractional Dunkl Laplacian
Established Bochner subordination representation
Formulated an extension problem for the operator
Abstract
In this paper, we present an approach to the fractional Dunkl Laplacian in a framework emerging from certain reflection symmetries in Euclidean spaces. Our main result is pointwise formulas, Bochner subordination, and an extension problem for the fractional Dunkl Laplacian as well
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Taxonomy
TopicsMathematical Analysis and Transform Methods · Medical Imaging Techniques and Applications · Microwave Imaging and Scattering Analysis