# The Weyl Operator and its Generalization

• Leon Cohen
Book

Part of the Pseudo-Differential Operators book series (PDO, volume 9)

1. Front Matter
Pages i-xii
2. Leon Cohen
Pages 1-4
3. Leon Cohen
Pages 5-24
4. Leon Cohen
Pages 25-46
5. Leon Cohen
Pages 47-59
6. Leon Cohen
Pages 61-67
7. Leon Cohen
Pages 69-84
8. Leon Cohen
Pages 85-90
9. Leon Cohen
Pages 91-94
10. Leon Cohen
Pages 95-101
11. Leon Cohen
Pages 103-106
12. Leon Cohen
Pages 107-110
13. Leon Cohen
Pages 111-119
14. Leon Cohen
Pages 121-128
15. Leon Cohen
Pages 129-130
16. Leon Cohen
Pages 131-149
17. Back Matter
Pages 151-159

### Introduction

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 century many isolated results were obtained. These developments were mostly based on associating a function of one variable with one operator, the operator generally being the differentiation operator. With the discovery of quantum mechanics in the years 1925-1930, there arose, in a natural way, the issue that one has to associate a function of two variables with a function of two operators that do not commute. Methods to do so became known as rules of association, correspondence rules, or ordering rules. This has led to a wonderfully rich mathematical development that has found applications in many fields. Subsequently it was realized that for every correspondence rule there is a corresponding phase-space distribution. Now the fields of correspondence rules and phase-space distributions are intimately connected. A similar development occurred in the field of time-frequency analysis where the aim is to understand signals with changing frequencies.

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.

#### Authors and affiliations

• Leon Cohen
• 1
1. 1.Hunter College & Graduate CenterCity University of New YorkNew YorkUSA

### Bibliographic information

• DOI https://doi.org/10.1007/978-3-0348-0294-9
• Copyright Information Springer Basel 2013
• Publisher Name Birkhäuser, Basel
• eBook Packages Mathematics and Statistics
• Print ISBN 978-3-0348-0293-2
• Online ISBN 978-3-0348-0294-9