000			04533nam a22005055i 4500
001			978-1-4614-8535-3
003			DE-He213
005			20140220082502.0
007			cr nn 008mamaa
008			131030s2014 xxu| s |||| 0|eng d
020			_a9781461485353 _9978-1-4614-8535-3
024	7		_a10.1007/978-1-4614-8535-3 _2doi
050		4	_aQC173.96-174.52
072		7	_aPHQ _2bicssc
072		7	_aSCI057000 _2bisacsh
082	0	4	_a530.12 _223
100	1		_aAli, Syed Twareque. _eauthor.
245	1	0	_aCoherent States, Wavelets, and Their Generalizations _h[electronic resource] / _cby Syed Twareque Ali, Jean-Pierre Antoine, Jean-Pierre Gazeau.
250			_a2nd ed. 2014.
264		1	_aNew York, NY : _bSpringer New York : _bImprint: Springer, _c2014.
300			_aXVIII, 577 p. 31 illus., 8 illus. in color. _bonline resource.
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
347			_atext file _bPDF _2rda
490	1		_aTheoretical and Mathematical Physics, _x1864-5879
505	0		_aCanonical 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.
520			_aThis 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, shearlets, etc.). In addition, it contains a new chapter on coherent state quantization and the related probabilistic aspects. As a survey of the theory of coherent states, wavelets, and some of their generalizations, it emphasizes mathematical principles, subsuming the theories of both wavelets and coherent states into a single analytic structure. The approach allows the user to take a classical-like view of quantum states in physics.   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 one to dispense with the group context altogether. In this context, wavelets can be generated from coherent states of the affine group of the real line, and higher-dimensional wavelets arise from coherent states of other groups. The unified background makes transparent an entire range of properties of wavelets and coherent states. Many concrete examples, such as coherent states from semisimple Lie groups, Gazeau-Klauder coherent states, coherent states for the relativity groups, and several kinds of wavelets, are discussed in detail. The book concludes with a palette of potential applications, from the quantum physically oriented, like the quantum-classical transition or the construction of adequate states in quantum information, to the most innovative techniques to be used in data processing.   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 first edition of the book is already a proven compendium for physicists and mathematicians active in the field, and with full coverage of the latest theory and results the revised second edition is even more valuable.
650		0	_aPhysics.
650		0	_aGroup theory.
650		0	_aQuantum theory.
650	1	4	_aPhysics.
650	2	4	_aQuantum Physics.
650	2	4	_aGroup Theory and Generalizations.
650	2	4	_aQuantum Information Technology, Spintronics.
700	1		_aAntoine, Jean-Pierre. _eauthor.
700	1		_aGazeau, Jean-Pierre. _eauthor.
710	2		_aSpringerLink (Online service)
773	0		_tSpringer eBooks
776	0	8	_iPrinted edition: _z9781461485346
830		0	_aTheoretical and Mathematical Physics, _x1864-5879
856	4	0	_uhttp://dx.doi.org/10.1007/978-1-4614-8535-3
912			_aZDB-2-PHA
999			_c92188 _d92188