A Group-Theoretic Construction with Spatiotemporal Wavelets for the Analysis of Rotational Motion
Journal of Mathematical Imaging and Vision
The Uncertainty Principle: Group Theoretic Approach, Possible Minimizers and Scale-Space Properties
Journal of Mathematical Imaging and Vision
Associated hypergeometric-type functions and coherent states
MATH'05 Proceedings of the 8th WSEAS International Conference on Applied Mathematics
Concurrence in the framework of coherent states
Quantum Information Processing
SSVM'07 Proceedings of the 1st international conference on Scale space and variational methods in computer vision
Scale-space generation via uncertainty principles
Scale-Space'05 Proceedings of the 5th international conference on Scale Space and PDE Methods in Computer Vision
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A survey of the theory of coherent states, wavelets, and some of their generalizations, emphasizing mathematical structures. Starting from the standard theory of coherent states over Lie groups, the authors generalize the formalism by associating coherent states to group representations that are square integrable over a homogeneous space; a further step allows the group context to be dispensed with altogether. The unified background makes transparent otherwise obscure properties of wavelets and of coherent states. Many concrete examples, such as semisimple Lie groups, the relativity group, and several kinds of wavelets, are discussed in detail. The book concludes with physical applications, centering on the quantum measurement problem and the quantum-classical transition. Intended as an introduction to current research for graduate students and others entering the field, the mathematical discussion is self- contained. With its extensive references to the research literature, the book will also be a useful compendium of recent results for physicists and mathematicians already active in the field.