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)
Access this book
Tax calculation will be finalised at checkout
Other ways to access
Table of contents (15 chapters)
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