منابع مشابه
On quaternionic functional analysis
In this article, we will show that the category of quaternion vector spaces, the category of (both one-sided and two sided) quaternion Hilbert spaces and the category of quaternion B∗-algebras are equivalent to the category of real vector spaces, the category of real Hilbert spaces and the category of real C∗-algebras respectively. We will also give a Riesz representation theorem for quaternion...
متن کاملQuaternionic Analysis
1. Introduction. The richness of the theory of functions over the complex field makes it natural to look for a similar theory for the only other non-trivial real asso-ciative division algebra, namely the quaternions. Such a theory exists and is quite far-reaching, yet it seems to be little known. It was not developed until nearly a century after Hamilton's discovery of quaternions. Hamilton him...
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The aim of this paper is to present the basics of a mathematical theory of a new Fourier transform of colour images from the point of view of Clifford analysis. Quaternionic-valued signals have long been used as a model for colour images and Fourier transforms for such signals have been studied in [3], [?], [6], [?], [7]. In this paper we use a version of the Fourier kernel markedly from those ...
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Properties of the Cauchy–Riemann–Fueter equation for maps between quaternionic manifolds are studied. Spaces of solutions in case of maps from a K3–surface to the cotangent bundle of a complex projective space are computed. A relationship between harmonic spinors of a generalized nonlinear Dirac operator and solutions of the Cauchy– Riemann–Fueter equation are established.
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We develop quaternionic analysis using as a guiding principle representation theory of various real forms of the conformal group. We first review the Cauchy-Fueter and Poisson formulas and explain their representation theoretic meaning. The requirement of unitarity of representations leads us to the extensions of these formulas in the Minkowski space, which can be viewed as another real form of...
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ژورنال
عنوان ژورنال: Mathematical Proceedings of the Cambridge Philosophical Society
سال: 2007
ISSN: 0305-0041,1469-8064
DOI: 10.1017/s0305004107000187