The quaternionic affine group and related continuous wavelet transforms on complex and quaternionic Hilbert spaces
نویسندگان
چکیده
منابع مشابه
Projective Group Representations in Quaternionic Hilbert Space
We extend the discussion of projective group representations in quaternionic Hilbert space which was given in our recent book. The associativity condition for quaternionic projective representations is formulated in terms of unitary operators and then analyzed in terms of their generator structure. The multi–centrality and centrality assumptions are also analyzed in generator terms, and implica...
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Some years ago, H. A. Jaffee found the real forms of Hermitian symmetric spaces ([J1], [J2]; or see [HÓ]). That classification turns out to be related to the classification of causal symmetric spaces. This was first observed by I. Satake ([S, Remark 2 on page 30] and [S, Remark on page 87]). Somewhat later, it was independently observed by J. Hilgert, G. Ólafsson and B. Ørsted; see [HÓ], especi...
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The main result is that any continuous real-linear operator A on a quaternionic Hubert space has a unique decomposition A=A0+iiAl + izAi+iiA3, where the A„ are continuous linear operators and (fi,f2,'3) is any right-handed orthonormal triad of vector quaternions. Other results concern the place of the colinear and complex-linear operators in this characterisation and the effect on the Av of a r...
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ژورنال
عنوان ژورنال: Journal of Mathematical Physics
سال: 2014
ISSN: 0022-2488,1089-7658
DOI: 10.1063/1.4881716