Heisenberg uncertainty principle for Gabor transform on compact extensions of Rn

We prove in this paper a generalization of Heisenberg inequality for Gabor transform in the setup of the semidirect product R n ⋊ K , where K is a compact subgroup of automorphisms of R n . We also solve the sharpness problem and thus we obtain an optimal analogue of the Heisenberg inequality. A loc...

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Bibliographic Details
Published inJournal of pseudo-differential operators and applications Vol. 15; no. 2
Main Authors Smaoui, Kais, Abid, Khouloud
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 01.06.2024
Springer Nature B.V
Subjects
Algebra
Analysis
Applications of Mathematics
Automorphisms
Functional Analysis
Gabor transformation
Mathematics
Mathematics and Statistics
Operator Theory
Partial Differential Equations
Subgroups
Uncertainty principles
Gabor transform
Uncertainty principle
43A32
Heisenberg inequality
22E30
43A30
Local uncertainty inequality
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Summary:We prove in this paper a generalization of Heisenberg inequality for Gabor transform in the setup of the semidirect product R n ⋊ K , where K is a compact subgroup of automorphisms of R n . We also solve the sharpness problem and thus we obtain an optimal analogue of the Heisenberg inequality. A local uncertainty inequality for the Gabor transform is also provided, in the same context. This allows us to prove a couple of global uncertainty inequalities. The representation theory and Plancherel formula are fundamental tools in the proof of our results.
ISSN:1662-9981
1662-999X
DOI:10.1007/s11868-024-00598-y