Uncertainty principles for the $q$-Hankel–Stockwell transform

Kamel Brahim; Hédi Ben Elmonser

doi:10.37863/umzh.v75i7.7166

Kamel Brahim Department of Mathematics, College of Science, University of Bisha, Saudi Arabia and Faculty of Sciences of Tunis, University of Tunis El Manar, Tunisia
Hédi Ben Elmonser Department of Mathematics, College of Science Al-Zul, Majmaah University, Al-Majmaah, Saudi Arabia and Department of Mathematics, National Institute of Technologie and Applied Sciences, Tunis, Tunisia

DOI: https://doi.org/10.37863/umzh.v75i7.7166

Keywords: q-Harmonic analysis, q-Hankel Stockwell transform, Uncertainty principles

Abstract

UDC 517.3

By using the $q$-Jackson integral and some elements of the $q$-harmonic analysis associated with the $q$-Hankel transform, we introduce and study a $q$-analog of the Hankel–Stockwell transform. We give some harmonic analysis properties (Plancherel formula, inversion formula, reproduicing kernel, etc.). Furthermore, we establish a version of Heisenberg's uncertainty principles. Finally, we study the $q$-Hankel–Stockwell transform on a subset of finite measure.

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