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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 Publication Applied Mathematics and Computation ISSN 00963003 Volume 247Pages: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. Keyword Asymptotic Behaviour Bochner-minlos Theorem Positive Definitely Measure Quaternion Linear Canonical Transform Quaternionic Analysis DOI 10.1016/j.amc.2014.08.090 URL View the original Indexed By SCIE Language 英語English WOS Research Area Mathematics WOS Subject Mathematics, Applied WOS ID WOS:000344474800058 Fulltext Access Citation statistics Cited Times [WOS]:29   [WOS Record]     [Related Records in WOS] Document Type Journal article Collection DEPARTMENT OF MATHEMATICS Affiliation 1.Universidade de Macau2.Universidade de Aveiro First Author Affilication University of Macau Recommended CitationGB/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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