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Asymptotic behaviour of the quaternion linear canonical transform and the Bochner-Minlos theorem
Kou K.I.1; Morais J.2
2014-11-15
Source PublicationApplied Mathematics and Computation
ISSN00963003
Volume247Pages:675-688
Abstract

There have been numerous proposals in the literature to generalize the classical Fourier transform by making use of the Hamiltonian quaternion algebra. The present paper reviews the quaternion linear canonical transform (QLCT) which is a generalization of the quaternion Fourier transform and it studies a number of its properties. In the first part of this paper, we establish a generalized Riemann-Lebesgue lemma for the (right-sided) QLCT. This lemma prescribes the asymptotic behaviour of the QLCT extending and refining the classical Riemann-Lebesgue lemma for the Fourier transform of 2D quaternion signals. We then introduce the QLCT of a probability measure, and we study some of its basic properties such as linearity, reconstruction formula, continuity, boundedness, and positivity. Finally, we extend the classical Bochner-Minlos theorem to the QLCT setting showing the applicability of our approach.

KeywordAsymptotic Behaviour Bochner-minlos Theorem Positive Definitely Measure Quaternion Linear Canonical Transform Quaternionic Analysis
DOI10.1016/j.amc.2014.08.090
URLView the original
Indexed BySCI
Language英语
WOS Research AreaMathematics
WOS SubjectMathematics, Applied
WOS IDWOS:000344474800058
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Citation statistics
Cited Times [WOS]:17   [WOS Record]     [Related Records in WOS]
Document TypeJournal article
CollectionDEPARTMENT OF MATHEMATICS
Affiliation1.Universidade de Macau
2.Universidade de Aveiro
Recommended Citation
GB/T 7714
Kou K.I.,Morais J.. Asymptotic behaviour of the quaternion linear canonical transform and the Bochner-Minlos theorem[J]. Applied Mathematics and Computation,2014,247:675-688.
APA Kou K.I.,&Morais J..(2014).Asymptotic behaviour of the quaternion linear canonical transform and the Bochner-Minlos theorem.Applied Mathematics and Computation,247,675-688.
MLA Kou K.I.,et al."Asymptotic behaviour of the quaternion linear canonical transform and the Bochner-Minlos theorem".Applied Mathematics and Computation 247(2014):675-688.
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