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Bochner-minlos theorem and quaternion Fourier transform
Georgiev S.3; Morais J.4; Kou K.I.2; Sprossig W.1
AbstractThere have been several attempts in the literature to generalize the classical Fourier transform by making use of the Hamiltonian quaternion algebra. The first part of this chapter features certain properties of the asymptotic behaviour of the quaternion Fourier transform. In the second part we introduce the quaternion Fourier transform of a probability measure, and we establish some of its basic properties. In the final analysis, we introduce the notion of positive definite measure, and we set out to extend the classical Bochner-Minlos theorem to the framework of quaternion analysis.
KeywordAsymptotic behaviour Bochner-Minlos theorem Positive definitely measure Quaternion analysis Quaternion fourier transform
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Affiliation1.Technische Universität Bergakademie Freiberg
2.Universidade de Macau
3.Sofia University St. Kliment Ohridski
4.Universidade de Aveiro
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GB/T 7714
Georgiev S.,Morais J.,Kou K.I.,et al. Bochner-minlos theorem and quaternion Fourier transform[M],2013.
APA Georgiev S.,Morais J.,Kou K.I.,&Sprossig W..(2013).Bochner-minlos theorem and quaternion Fourier transform. .
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