Asymptotic Behaviour of the Quaternion Linear Canonical Tlansform and the Bochner-Minlos Theorem

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	Asymptotic Behaviour of the Quaternion Linear Canonical Tlansform and the Bochner-Minlos Theorem
	Kou, K. I.; Morais, J.
	2014-11-15
Source Publication	Applied Mathematics and Computation
ISSN	0096-3003
Pages	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	Quaternionic analysis Quaternion linear canonical transform Asymptotic behaviour Positive definitely measure Bochner–Minlos theorem
Language	英語English
The Source to Article	PB_Publication
PUB ID	14222
Document Type	Journal article
Collection	DEPARTMENT OF MATHEMATICS
Corresponding Author	Kou, K. I.
Recommended Citation GB/T 7714	Kou, K. I.,Morais, J.. Asymptotic Behaviour of the Quaternion Linear Canonical Tlansform and the Bochner-Minlos Theorem[J]. Applied Mathematics and Computation, 2014, 675-688.
APA	Kou, K. I.., & Morais, J. (2014). Asymptotic Behaviour of the Quaternion Linear Canonical Tlansform and the Bochner-Minlos Theorem. Applied Mathematics and Computation, 675-688.
MLA	Kou, K. I.,et al."Asymptotic Behaviour of the Quaternion Linear Canonical Tlansform and the Bochner-Minlos Theorem".Applied Mathematics and Computation (2014):675-688.

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