Overview
- Numerous examples are worked, out illustrating each result
- The applications to various fields are discussed in elementary fashion
- The methods are extended to operators other than the standard ones
- Includes supplementary material: sn.pub/extras
Part of the book series: Pseudo-Differential Operators (PDO)
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Table of contents (15 chapters)
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Front Matter
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Back Matter
Keywords
About this book
The discovery of quantum mechanics in the years 1925-1930 necessitated the consideration of associating ordinary functions with non-commuting operators. Methods were proposed by Born/Jordan, Kirkwood, and Weyl. Sometime later, Moyal saw the connection between the Weyl rule and the Wigner distribution, which had been proposed by Wigner in 1932 as a way of doing quantum statistical mechanics. The basic idea of associating functions with operators has since been generalized and developed to a high degree. It has found several application fields, including quantum mechanics, pseudo-differential operators, time-frequency analysis, quantum optics, wave propagation, differential equations, image processing, radar, and sonar.
This book aims at bringing together the results from the above mentioned fields in a unified manner and showing the reader how the methods have been applied. 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.
Authors and Affiliations
Bibliographic Information
Book Title: The Weyl Operator and its Generalization
Authors: Leon Cohen
Series Title: Pseudo-Differential Operators
DOI: https://doi.org/10.1007/978-3-0348-0294-9
Publisher: Birkhäuser Basel
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Basel 2013
Softcover ISBN: 978-3-0348-0293-2Published: 12 December 2012
eBook ISBN: 978-3-0348-0294-9Published: 13 December 2012
Series ISSN: 2297-0355
Series E-ISSN: 2297-0363
Edition Number: 1
Number of Pages: XII, 159
Topics: Partial Differential Equations, Operator Theory, Mathematical Physics