LEADER 05471nam 22007335 450 001 9910736987803321 005 20200630152207.0 010 $a1-4614-8535-5 024 7 $a10.1007/978-1-4614-8535-3 035 $a(CKB)3710000000057103 035 $a(EBL)1592895 035 $a(OCoLC)880589395 035 $a(SSID)ssj0001049399 035 $a(PQKBManifestationID)11661880 035 $a(PQKBTitleCode)TC0001049399 035 $a(PQKBWorkID)11019081 035 $a(PQKB)11398566 035 $a(MiAaPQ)EBC1592895 035 $a(DE-He213)978-1-4614-8535-3 035 $a(PPN)17609900X 035 $a(EXLCZ)993710000000057103 100 $a20131030d2014 u| 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aCoherent States, Wavelets, and Their Generalizations$b[electronic resource] /$fby Syed Twareque Ali, Jean-Pierre Antoine, Jean-Pierre Gazeau 205 $a2nd ed. 2014. 210 1$aNew York, NY :$cSpringer New York :$cImprint: Springer,$d2014. 215 $a1 online resource (586 p.) 225 1 $aTheoretical and Mathematical Physics,$x1864-5879 300 $aDescription based upon print version of record. 311 $a1-4614-8534-7 320 $aIncludes bibliographical references and index. 327 $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. 330 $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. 410 0$aTheoretical and Mathematical Physics,$x1864-5879 606 $aQuantum physics 606 $aGroup theory 606 $aQuantum computers 606 $aSpintronics 606 $aQuantum Physics$3https://scigraph.springernature.com/ontologies/product-market-codes/P19080 606 $aGroup Theory and Generalizations$3https://scigraph.springernature.com/ontologies/product-market-codes/M11078 606 $aQuantum Information Technology, Spintronics$3https://scigraph.springernature.com/ontologies/product-market-codes/P31070 615 0$aQuantum physics. 615 0$aGroup theory. 615 0$aQuantum computers. 615 0$aSpintronics. 615 14$aQuantum Physics. 615 24$aGroup Theory and Generalizations. 615 24$aQuantum Information Technology, Spintronics. 676 $a586 686 $a81-02, 81R30, 42C40$2msc 700 $aAli$b Syed Twareque$4aut$4http://id.loc.gov/vocabulary/relators/aut$048963 702 $aAntoine$b Jean-Pierre$4aut$4http://id.loc.gov/vocabulary/relators/aut 702 $aGazeau$b Jean-Pierre$4aut$4http://id.loc.gov/vocabulary/relators/aut 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910736987803321 996 $aCoherent States, Wavelets, and Their Generalizations$93424612 997 $aUNINA