By Gerald B. Folland
A path in summary Harmonic Analysis is an advent to that a part of research on in the neighborhood compact teams that may be performed with minimum assumptions at the nature of the gang. As a generalization of classical Fourier research, this summary concept creates a beginning for loads of glossy research, and it includes a variety of based effects and methods which are of curiosity of their personal correct.
This ebook develops the summary thought in addition to a well-chosen choice of concrete examples that exemplify the implications and exhibit the breadth in their applicability. After a initial bankruptcy containing the required history fabric on Banach algebras and spectral conception, the textual content units out the final conception of in the neighborhood compact teams and their unitary representations, by way of a improvement of the extra particular concept of research on Abelian teams and compact teams. there's an in depth bankruptcy at the concept of brought about representations and its functions, and the publication concludes with a extra casual exposition at the thought of representations of non-Abelian, non-compact groups.
Featuring vast updates and new examples, the Second Edition:
- Adds a brief part on von Neumann algebras
- Includes Mark Kac’s uncomplicated facts of a limited type of Wiener’s theorem
- Explains the relation among SU(2) and SO(3) when it comes to quaternions, a sublime strategy that brings SO(4) into the image with little effort
- Discusses representations of the discrete Heisenberg team and its valuable quotients, illustrating the Mackey computing device for normal semi-direct items and the pathological phenomena for nonregular ones
A direction in summary Harmonic research, moment version serves as an entrée to complicated arithmetic, providing the necessities of harmonic research on in the community compact teams in a concise and available form.
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Extra resources for A Course in Abstract Harmonic Analysis, Second Edition (Textbooks in Mathematics)
A Course in Abstract Harmonic Analysis, Second Edition (Textbooks in Mathematics) by Gerald B. Folland