Coherent States, Wavelets, and Their Generalizations

• Main Authors: Ali, Syed Twareque (Author), Antoine, Jean-Pierre (Author), Gazeau, Jean-Pierre (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: New York, NY : Springer New York : Imprint: Springer, 2014.
• Edition: 2nd ed. 2014.
• Series: Theoretical and Mathematical Physics,
• Subjects: Physics.; Group theory.; Quantum physics.; Quantum computers.; Spintronics.; Quantum Physics.; Group Theory and Generalizations.; Quantum Information Technology, Spintronics.

This second edition is fully updated, covering in particular new types of coherent states (the so-called Gazeau-Klauder coherent states, nonlinear coherent states, squeezed states, as used now routinely in quantum optics) and various generalizations of wavelets (wavelets on manifolds, curvelets, she...

Table of Contents:

• 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
• CS Quantizations and Probabilistic Aspects
• Direct Wavelet Transforms
• Multidimensional Wavelets
• Wavelets Related to Other G Groups
• The Discretization Problem - Frames Sampling and All That.