Gabor System based on the unitary dual of the Heisenberg group

被引：0
|
作者：
Das, Santi R. [2 ]
Ramakrishnan, Radha [1 ]
机构：
[1] Indian Inst Technol, Dept Math, Madras, India
[2] OCC Homi Bhabha Natl Inst, NISER Bhubaneswar, Sch Math Sci, Jatni 752050, India
来源：
FORUM MATHEMATICUM | 2025年
关键词：
Bessel sequence; frames; Gabor system; Heisenberg group; Hilbert-Schmidt operator; orthonormal system; Parseval frame; Riesz basis; unitary representation; Weyl transform; SHIFT-INVARIANT SPACES; WAVELET SYSTEM; FRAMES;
D O I：
10.1515/forum-2024-0385
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, the Gabor system based on the unitary dual of the Heisenberg group Hn is introduced and a sufficient condition is obtained for the Gabor system to be a Bessel sequence for L 2 (& Ropf;& lowast; , B2; d kappa) using the Schr & ouml;dinger representation of Hn , where B2 denotes the class of Hilbert-Schmidt operators on L 2 (& Ropf;n ) and d kappa denotes the Haar measure on & Ropf;& lowast; . 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.
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页数：21
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