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The Weyl Operator and its Generalization
ISBN-13:
9783034802949
Veröffentl:
2012
Seiten:
159
Autor:
Leon Cohen
Serie:
Pseudo-Differential Operators
eBook Typ:
PDF
eBook Format:
EPUB
Kopierschutz:
1 - PDF Watermark
Sprache:
Englisch
Beschreibung:
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.
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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