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Bochner-minlos theorem and quaternion Fourier transform
Georgiev,S.1; Morais,J.2; Kou,K. I.3; Sprößig,W.4
Source PublicationQuaternion and Clifford Fourier Transforms and Wavelets
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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Scopus ID2-s2.0-84978158036
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Document TypeBook chapter
Corresponding AuthorGeorgiev,S.
Affiliation1.Department of Differential Equations,University of Sofia,Sofia,Bulgaria
2.Centro de Investigacao e Desenvolvimento em Matematica e Aplicaœes (CIDMA),Universidade de Aveiro,Aveiro,3810-193,Portugal
3.Department of Mathematics,Faculty of Science and Technology,University of Macau,Macao
4.Freiberg University of Mining and Technology,Freiberg,Germany
Recommended Citation
GB/T 7714
Georgiev,S.,Morais,J.,Kou,K. I.,et al. Bochner-minlos theorem and quaternion Fourier transform,2013:105-120.
APA Georgiev,S.,Morais,J.,Kou,K. I.,&Sprößig,W..(2013).Bochner-minlos theorem and quaternion Fourier transform.Quaternion and Clifford Fourier Transforms and Wavelets,105-120.
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