Coherent States, Wavelets and Their Generalizations: A Mathematical Overview - Rilegato

Ali, S. Twareque; Antoine, Jean Pierre; Gazeau, Jean-Pierre

Rilegato

ISBN 10: 0387989080 ISBN 13: 9780387989082

Casa editrice: Springer Verlag, 2000

Riassunto

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.

Su questo libro

Recensione

From the reviews:

"The subject of coherent states and/or wavelets (CS-W) is a hot topic for decades. ... Personally I prefer the book under review to many other ones published before. ... It is clearly written, mathematically sound and well illustrated ... . Short but informative historical remarks in the text additionally guide through the literature. The index is useful too. ... I recommend this book to everyone who wishes to learn CS-W, or already works in the area, or just needs a good reference source." (Vladimir V. Kisil, Zentralblatt MATH, Vol. 1064, 2005)

Contenuti

Preface.- Introduction.- Canonical Coherent States.- Positive Operator-Valued Measures and Frames.- Some Group Theory.- Hilbert Spaces.- Square Integrable and Holomorphic Kernels.- Covariant Coherent States.- Coherent States from Square Integrable Representations.- Some Examples and Generalizations.- CS of General Semidirect Product Groups.- CS of Product Groups.- Wavelets.- Discrete Wavelet Transforms.- Multidimensional Wavelets.- Wavelets Related to Other G Groups.- The Discretiaztion Problem: Frames Sampling, and all that.- Conclusion.

Dettagli dell'edizione

• Editore: Springer Verlag
• Data di pubblicazione: 2000
• Lingua: Inglese
• ISBN 10: 0387989080
• ISBN 13: 9780387989082
• Rilegatura: Copertina rigida
• Numero di pagine: 418
• Contatto del produttore: non disponibile
• Persona responsabile: CMN Printpool Inh. Mathis Neumann; https://www.also.com/ec/cms5/en_6000/6000/index.jsp; ; Friedrich-Karl-Str. 9; Hamburg; Germania