CHARACTERIZATIONS OF THE MULTIVARIATE WAVE PACKET SYSTEMS

Some characterizations of the multivariate wave packet systems in terms of the Fourier transforms of the wave packet systems' generating functions are discussed in this paper. First, the characterizations of the orthogonal wave packet systems are provided. Secondly, a sufficient condition of th...

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Bibliographic Details
Published inTaiwanese journal of mathematics Vol. 18; no. 5; pp. 1389 - 1409
Main Authors Wu, Guochang, Li, Dengfeng
Format Journal Article
LanguageEnglish
Published Mathematical Society of the Republic of China 01.10.2014
Subjects
Fourier transformations
Generating function
Harmonic analysis
Mathematical functions
Necessary conditions
Operator theory
Sufficient conditions
Wave packets
Wavelet analysis
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ISSN1027-5487
2224-6851
2224-6851
DOI10.11650/tjm.18.2014.4195

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Summary:Some characterizations of the multivariate wave packet systems in terms of the Fourier transforms of the wave packet systems' generating functions are discussed in this paper. First, the characterizations of the orthogonal wave packet systems are provided. Secondly, a sufficient condition of the completeness of wave packet system in some special cases is established. Finally, the necessary conditions and sufficient conditions for the wave packet systems to be wave packet Parseval frames with the very general lattices are obtained. Thus, the corresponding known results in Gabor systems and wavelet systems are obtained as some corollaries. 2010Mathematics Subject Classification: 42C15, 42C40. Key words and phrases: Gabor system, Wavelet system, The wave packet system.
ISSN:1027-5487
2224-6851
2224-6851
DOI:10.11650/tjm.18.2014.4195