The Resource The Weyl Operator and its generalization, Leon Cohen
The Weyl Operator and its generalization, Leon Cohen
Resource Information
The item The Weyl Operator and its generalization, Leon Cohen represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Missouri Libraries.This item is available to borrow from 1 library branch.
Resource Information
The item The Weyl Operator and its generalization, Leon Cohen represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Missouri Libraries.
This item is available to borrow from 1 library branch.
 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 19251930, 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 phasespace distribution. Now the fields of correspondence rules and phasespace distributions are intimately connected. A similar development occurred in the field of timefrequency 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 uptodate working knowledge of the field. The mathematics is accessible to the uninitiated reader and is presented in a straightforward manner
 Language
 eng
 Extent
 1 online resource.
 Contents

 TimeFrequency Operators
 Transformation of Differential Equations Into Phase Space
 The Eigenvalue Problem in PhaseSpace
 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 PhaseSpace 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  PhaseSpace 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
 Isbn
 9783034802949
 Label
 The Weyl Operator and its generalization
 Title
 The Weyl Operator and its generalization
 Statement of responsibility
 Leon Cohen
 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 19251930, 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 phasespace distribution. Now the fields of correspondence rules and phasespace distributions are intimately connected. A similar development occurred in the field of timefrequency 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 uptodate working knowledge of the field. The mathematics is accessible to the uninitiated reader and is presented in a straightforward manner
 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
 Pseudodifferential 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
 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

 TimeFrequency Operators
 Transformation of Differential Equations Into Phase Space
 The Eigenvalue Problem in PhaseSpace
 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 PhaseSpace 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  PhaseSpace 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
 10.1007/9783034802949
 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
 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

 TimeFrequency Operators
 Transformation of Differential Equations Into Phase Space
 The Eigenvalue Problem in PhaseSpace
 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 PhaseSpace 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  PhaseSpace 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
 10.1007/9783034802949
 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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