This book develops the abstract theory along with a well-chosen selection of concrete examples that exemplify the results and show the breadth of their applicability. After a preliminary chapter containing the necessary background material on Banach algebras and spectral theory, the text sets out the general theory of locally compact groups and their unitary representations, followed by a development of the more specific theory of analysis on Abelian groups and compact groups. There is an extensive chapter on the theory of induced representations and its applications, and the book concludes with a more informal exposition on the theory of representations of non-Abelian, non-compact groups.
Featuring extensive updates and new examples, the Second Edition:
- Adds a short section on von Neumann algebras
- Includes Mark Kac’s simple proof of a restricted form of Wiener’s theorem
- Explains the relation between SU(2) and SO(3) in terms of quaternions, an elegant method that brings SO(4) into the picture with little effort
- Discusses representations of the discrete Heisenberg group and its central quotients, illustrating the Mackey machine for regular semi-direct products and the pathological phenomena for nonregular ones
A Course in Abstract Harmonic Analysis, Second Edition serves as an entrée to advanced mathematics, presenting the essentials of harmonic analysis on locally compact groups in a concise and accessible form.
This book develops the abstract theory along with a well-chosen selection of concrete examples that exemplify the results and show the breadth of their applicability. After a preliminary chapter containing the necessary background material on Banach algebras and spectral theory, the text sets out the general theory of locally compact groups and their unitary representations, followed by a development of the more specific theory of analysis on Abelian groups and compact groups. There is an extensive chapter on the theory of induced representations and its applications, and the book concludes with a more informal exposition on the theory of representations of non-Abelian, non-compact groups.
Featuring extensive updates and new examples, the Second Edition:
- Adds a short section on von Neumann algebras
- Includes Mark Kac’s simple proof of a restricted form of Wiener’s theorem
- Explains the relation between SU(2) and SO(3) in terms of quaternions, an elegant method that brings SO(4) into the picture with little effort
- Discusses representations of the discrete Heisenberg group and its central quotients, illustrating the Mackey machine for regular semi-direct products and the pathological phenomena for nonregular ones
A Course in Abstract Harmonic Analysis, Second Edition serves as an entrée to advanced mathematics, presenting the essentials of harmonic analysis on locally compact groups in a concise and accessible form.
A Course in Abstract Harmonic Analysis
320
A Course in Abstract Harmonic Analysis
320Hardcover(Revised)
Product Details
| ISBN-13: | 9781498727136 |
|---|---|
| Publisher: | Taylor & Francis |
| Publication date: | 09/25/2015 |
| Series: | Textbooks in Mathematics , #29 |
| Edition description: | Revised |
| Pages: | 320 |
| Product dimensions: | 6.20(w) x 9.10(h) x 0.90(d) |