The Weyl Operator and its Generalization

• Main Author: Cohen, Leon. (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic
• Language: English
• Published: Basel : Springer Basel : Imprint: Birkhũser, 2013.
• Series: Pseudo-Differential Operators, Theory and Applications ; 9
• Subjects: Mathematics.; Operator theory.; Differential equations, partial.; Partial Differential Equations.; Operator Theory.; Mathematical Physics.
• Online Access: https://ezaccess.library.uitm.edu.my/login?url=http://dx.doi.org/10.1007/978-3-0348-0294-9

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...

Table of Contents:

• 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.