Year: 2025
Type: article
Abstract: In this paper, the Gabor system based on the unitary dual of the Heisenberg group H n \mathbb{H}^{n} is introduced and a sufficient condition is obtained for the Gabor system to be a Bessel sequence for L 2 ( R ∗ , B 2 ; d κ ) L^{2}(\mathbb{R}^{*},{\mathcal{B}_{2}};d\kappa) using the Schrödinger representation of H n \mathbb{H}^{n} , where B 2 \mathcal{B}_{2} denotes the class of Hilbert–Schmidt operators on L 2 ( R n ) L^{2}(\mathbb{R}^{n}) and d κ d\kappa denotes the Haar measure on R ∗ \mathbb{R}^{*} . Further, a necessary and sufficient condition is provided for the Gabor system to be an orthonormal system, a Parseval frame sequence, a frame sequence and a Riesz sequence.
Source: Forum Mathematicum
Authors: Santi R. Das, Radha Ramakrishnan
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4408905603