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The Resource The Weyl Operator and its generalization, Leon Cohen

The Weyl Operator and its generalization, Leon Cohen

Label
The Weyl Operator and its generalization
Title
The Weyl Operator and its generalization
Statement of responsibility
Leon Cohen
Creator
Subject
Language
eng
Summary
This book deals with the theory and application of associating a function of two variables with a function of two operators that do not commute. The concept of associating ordinary functions with operators has arisen in many areas of science and mathematics, and up to the beginning of the twentieth century many isolated results were obtained. These developments were mostly based on associating a function of one variable with one operator, the operator generally being the differentiation operator. With the discovery of quantum mechanics in the years 1925-1930, there arose, in a natural way, the issue that one has to associate a function of two variables with a function of two operators that do not commute. Methods to do so became known as rules of association, correspondence rules, or ordering rules. This has led to a wonderfully rich mathematical development that has found applications in many fields. Subsequently it was realized that for every correspondence rule there is a corresponding phase-space distribution. Now the fields of correspondence rules and phase-space distributions are intimately connected. A similar development occurred in the field of time-frequency analysis where the aim is to understand signals with changing frequencies. The Weyl Operator and Its Generalization aims at bringing together the basic results of the field in a unified manner. A wide audience is addressed, particularly students and researchers who want to obtain an up-to-date working knowledge of the field. The mathematics is accessible to the uninitiated reader and is presented in a straightforward manner
Member of
Cataloging source
GW5XE
http://library.link/vocab/creatorDate
1940-
http://library.link/vocab/creatorName
Cohen, Leon
Dewey number
530.15607
Index
index present
LC call number
QA689
LC item number
.C64 2013
Literary form
non fiction
Nature of contents
  • dictionaries
  • bibliography
Series statement
Pseudo-differential operators, theory and applications
Series volume
v. 9
http://library.link/vocab/subjectName
  • Generalized spaces
  • Mathematical physics
  • SCIENCE
  • Generalized spaces
  • Mathematical physics
Label
The Weyl Operator and its generalization, Leon Cohen
Instantiates
Publication
Antecedent source
unknown
Bibliography note
Includes bibliographical references and index
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Color
multicolored
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
  • Time-Frequency Operators
  • Transformation of Differential Equations Into Phase Space
  • The Eigenvalue Problem in Phase-Space
  • Arbitrary Operators: Single Operator
  • Uncertainty Principle for Arbitrary Operators
  • The Khintchine Theorem and Characteristic Function Representability
  • Arbitrary operators: Two Operators
  • Introduction and Terminology
  • Operator Algebra
  • The Weyl Operator
  • Generalized Operator Association
  • Generalized Phase-Space Distributions
  • Special Cases
  • Unitary Transformation
  • Path Integral Approach
  • Introduction -- The Fundamental Idea, Terminology, and Operator Algebra -- The Weyl Operator -- The Algebra of the Weyl Operator -- Product of Operators, Commutators, and the Moyal Sin Bracket -- Some Other Ordering Rules -- Generalized Operator Association -- The Fourier, Monomial, and Delta Function Associations -- Transformation Between Associations -- Path Integral Approach -- The Distribution of a Symbol and Operator -- The Uncertainty Principle -- Phase-Space Distributions -- Amplitude, Phase, Instantaneous Frequency, and the Hilbert Transform -- Time -- Frequency Analysis -- The Transformation of Differential Equations into Phase Space -- The Representation of Functions -- The N Operator Case
Control code
822976870
Dimensions
unknown
Extent
1 online resource.
File format
unknown
Form of item
online
Isbn
9783034802949
Level of compression
unknown
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Other control number
10.1007/978-3-0348-0294-9
http://library.link/vocab/ext/overdrive/overdriveId
424712
Quality assurance targets
not applicable
Reformatting quality
unknown
Sound
unknown sound
Specific material designation
remote
System control number
(OCoLC)822976870
Label
The Weyl Operator and its generalization, Leon Cohen
Publication
Antecedent source
unknown
Bibliography note
Includes bibliographical references and index
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Color
multicolored
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
  • Time-Frequency Operators
  • Transformation of Differential Equations Into Phase Space
  • The Eigenvalue Problem in Phase-Space
  • Arbitrary Operators: Single Operator
  • Uncertainty Principle for Arbitrary Operators
  • The Khintchine Theorem and Characteristic Function Representability
  • Arbitrary operators: Two Operators
  • Introduction and Terminology
  • Operator Algebra
  • The Weyl Operator
  • Generalized Operator Association
  • Generalized Phase-Space Distributions
  • Special Cases
  • Unitary Transformation
  • Path Integral Approach
  • Introduction -- The Fundamental Idea, Terminology, and Operator Algebra -- The Weyl Operator -- The Algebra of the Weyl Operator -- Product of Operators, Commutators, and the Moyal Sin Bracket -- Some Other Ordering Rules -- Generalized Operator Association -- The Fourier, Monomial, and Delta Function Associations -- Transformation Between Associations -- Path Integral Approach -- The Distribution of a Symbol and Operator -- The Uncertainty Principle -- Phase-Space Distributions -- Amplitude, Phase, Instantaneous Frequency, and the Hilbert Transform -- Time -- Frequency Analysis -- The Transformation of Differential Equations into Phase Space -- The Representation of Functions -- The N Operator Case
Control code
822976870
Dimensions
unknown
Extent
1 online resource.
File format
unknown
Form of item
online
Isbn
9783034802949
Level of compression
unknown
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Other control number
10.1007/978-3-0348-0294-9
http://library.link/vocab/ext/overdrive/overdriveId
424712
Quality assurance targets
not applicable
Reformatting quality
unknown
Sound
unknown sound
Specific material designation
remote
System control number
(OCoLC)822976870

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