Riesz transforms for the Dunkl harmonic oscillator
Adam Nowak, Krzysztof Stempak
TL;DR
This paper introduces and studies Riesz transforms associated with the Dunkl harmonic oscillator, expanding the mathematical understanding of harmonic analysis in this context.
Contribution
It defines and investigates a new system of Riesz transforms linked to the Dunkl harmonic oscillator, contributing novel theoretical insights.
Findings
Established boundedness properties of the Riesz transforms
Connected the transforms to harmonic analysis frameworks
Provided foundational results for further research
Abstract
We define and investigate a system of Riesz transforms related to the Dunkl harmonic oscillator.
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Taxonomy
TopicsMathematical Analysis and Transform Methods · Quantum Mechanics and Non-Hermitian Physics · Optical and Acousto-Optic Technologies