Wave packet frames in linear canonical domains: construction and perturbation: Wave packet frames in linear canonical domains

The wave packet systems are generated by the combined action of translation, dilation and modulation on a single function while frames are basis-like systems that span a vector space with linearly dependency. The main goal of the study is to intervene the advantages of both the frames and wave packe...

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Bibliographic Details
Published in:Journal of pseudo-differential operators and applications 2024, Vol.15 (4)
Main Authors: Teali, Aajaz A., Shah, Firdous A.
Format: Article
Language:English
Subjects:
Algebra
Analysis
Applications of Mathematics
Functional Analysis
Mathematics
Mathematics and Statistics
Operator Theory
Partial Differential Equations
Online Access:Get full text
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Summary:The wave packet systems are generated by the combined action of translation, dilation and modulation on a single function while frames are basis-like systems that span a vector space with linearly dependency. The main goal of the study is to intervene the advantages of both the frames and wave packets in the linear canonical domains. Besides, the construction of linear canonical wave packet system we present a necessary and sufficient condition for the linear canonical wave packet system to be a frame in the Hilbert space. Moreover, we study perturbation analysis of these canonical wave packet frame inequalities when the dilation and translation parameters are perturbed. The introduced frame inequalities are in terms of the linear canonical transform of the wave packet system’s, inheriting all the classical frame inequalities such as Gabor, wavelet, wave packet, and fractional wave packet inequalities.
ISSN:1662-9981
1662-999X
DOI:10.1007/s11868-024-00645-8