Localization Operators and Scalogram Associated with the Deformed Hankel Wavelet Transform

The deformed Hankel wavelet transform (( k ,  n )-HWT) is a novel addition to the class of wavelet transforms, which has gained a respectable status in the realm of time-frequency signal analysis within a short span of time. Knowing the fact that the study of localization operators is both theoretic...

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Bibliographic Details
Published inMediterranean journal of mathematics Vol. 20; no. 3
Main Authors Mejjaoli, Hatem, Trimèche, Khalifa
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 01.06.2023
Springer Nature B.V
Subjects
Deformation
Localization
Mathematics
Mathematics and Statistics
Operators
Signal analysis
Time-frequency analysis
Wavelet transforms
44A15
43A32
47G10
42B10
Deformed Hankel transform
localization operators
reproducing kernel
42A38
deformed Hankel wavelet transform
scalogram
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ISSN1660-5446
1660-5454
DOI10.1007/s00009-023-02325-1

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Summary:The deformed Hankel wavelet transform (( k ,  n )-HWT) is a novel addition to the class of wavelet transforms, which has gained a respectable status in the realm of time-frequency signal analysis within a short span of time. Knowing the fact that the study of localization operators is both theoretically interesting and practically useful, we investigated several subjects of time-frequency analysis for the deformed Hankel wavelet transform. First, we study the L p boundedness and compactness of localization operators associated with the deformed Hankel wavelet transforms on R . Next, involving the reproducing kernel and spectral theories we investigate the time-frequency operators. Finally, the scalogram for the deformed Hankel wavelet transform is introduced and studied at the end.
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ISSN:1660-5446
1660-5454
DOI:10.1007/s00009-023-02325-1