The Resource Coherent States, Wavelets, and Their Generalizations, by Syed Twareque Ali, Jean-Pierre Antoine, Jean-Pierre Gazeau, (electronic resource)

Coherent States, Wavelets, and Their Generalizations, by Syed Twareque Ali, Jean-Pierre Antoine, Jean-Pierre Gazeau, (electronic resource)

Label
Coherent States, Wavelets, and Their Generalizations
Title
Coherent States, Wavelets, and Their Generalizations
Statement of responsibility
by Syed Twareque Ali, Jean-Pierre Antoine, Jean-Pierre Gazeau
Creator
Contributor
Author
Author
Subject
Language
  • eng
  • eng
Summary
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, 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
Member of
http://library.link/vocab/creatorName
Ali, Syed Twareque
Dewey number
530.12
http://bibfra.me/vocab/relation/httpidlocgovvocabularyrelatorsaut
  • d6sVGv7DTbs
  • xlk27L0982o
  • 6ooTyUXcobU
Language note
English
LC call number
QC173.96-174.52
Literary form
non fiction
Nature of contents
dictionaries
http://library.link/vocab/relatedWorkOrContributorName
  • Antoine, Jean-Pierre.
  • Gazeau, Jean-Pierre.
Series statement
Theoretical and Mathematical Physics,
http://library.link/vocab/subjectName
  • Quantum physics
  • Group theory
  • Quantum computers
  • Spintronics
  • Quantum Physics
  • Group Theory and Generalizations
  • Quantum Information Technology, Spintronics
Label
Coherent States, Wavelets, and Their Generalizations, by Syed Twareque Ali, Jean-Pierre Antoine, Jean-Pierre Gazeau, (electronic resource)
Instantiates
Publication
Note
Description based upon print version of record
Bibliography note
Includes bibliographical references and index
Carrier category
online resource
Carrier category code
  • cr
Content category
text
Content type code
  • txt
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
Dimensions
unknown
Edition
2nd ed.
Extent
1 online resource (586 p.)
Form of item
online
Isbn
9781461485353
Media category
computer
Media type code
  • c
Other control number
10.1007/978-1-4614-8535-3
Specific material designation
remote
System control number
  • (CKB)3710000000057103
  • (EBL)1592895
  • (OCoLC)880589395
  • (SSID)ssj0001049399
  • (PQKBManifestationID)11661880
  • (PQKBTitleCode)TC0001049399
  • (PQKBWorkID)11019081
  • (PQKB)11398566
  • (MiAaPQ)EBC1592895
  • (DE-He213)978-1-4614-8535-3
  • (EXLCZ)993710000000057103
Label
Coherent States, Wavelets, and Their Generalizations, by Syed Twareque Ali, Jean-Pierre Antoine, Jean-Pierre Gazeau, (electronic resource)
Publication
Note
Description based upon print version of record
Bibliography note
Includes bibliographical references and index
Carrier category
online resource
Carrier category code
  • cr
Content category
text
Content type code
  • txt
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
Dimensions
unknown
Edition
2nd ed.
Extent
1 online resource (586 p.)
Form of item
online
Isbn
9781461485353
Media category
computer
Media type code
  • c
Other control number
10.1007/978-1-4614-8535-3
Specific material designation
remote
System control number
  • (CKB)3710000000057103
  • (EBL)1592895
  • (OCoLC)880589395
  • (SSID)ssj0001049399
  • (PQKBManifestationID)11661880
  • (PQKBTitleCode)TC0001049399
  • (PQKBWorkID)11019081
  • (PQKB)11398566
  • (MiAaPQ)EBC1592895
  • (DE-He213)978-1-4614-8535-3
  • (EXLCZ)993710000000057103

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