The Weyl Operator and its Generalization

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...

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Cohen, Leon (Autor)
Autor Corporativo: SpringerLink (Online service)
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Basel : Springer Basel : Imprint: Birkhäuser, 2013.
Edición:1st ed. 2013.
Colección:Pseudo-Differential Operators, Theory and Applications,
Temas:
Differential equations.
Operator theory.
Mathematical physics.
Differential Equations.
Operator Theory.
Mathematical Physics.
Acceso en línea:Texto Completo
Tabla de Contenidos:
  • 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.

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