Coherent States, Wavelets, and Their Generalizations
A Mathematical Overview
Seiten
2000
|
2000 ed.
Springer-Verlag New York Inc.
978-0-387-98908-2 (ISBN)
Springer-Verlag New York Inc.
978-0-387-98908-2 (ISBN)
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Wavelets have become an important analytical tool in signal processing and other applications. This book presents a unified survey of the theories of coherent states, wavelets, and some of their generalizations, emphasizing mathematical structures. It is useful as an introduction to research for graduate students and others entering the field.
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.
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.
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.
| Erscheint lt. Verlag | 1.1.2000 |
|---|---|
| Reihe/Serie | Graduate Texts in Contemporary Physics |
| Zusatzinfo | 1 black & white tables |
| Verlagsort | New York, NY |
| Sprache | englisch |
| Maße | 155 x 235 mm |
| Gewicht | 857 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Analysis |
| Naturwissenschaften ► Physik / Astronomie ► Astronomie / Astrophysik | |
| Naturwissenschaften ► Physik / Astronomie ► Atom- / Kern- / Molekularphysik | |
| Naturwissenschaften ► Physik / Astronomie ► Hochenergiephysik / Teilchenphysik | |
| Naturwissenschaften ► Physik / Astronomie ► Quantenphysik | |
| Naturwissenschaften ► Physik / Astronomie ► Theoretische Physik | |
| ISBN-10 | 0-387-98908-0 / 0387989080 |
| ISBN-13 | 978-0-387-98908-2 / 9780387989082 |
| Zustand | Neuware |
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