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 crowd. As a generalization of classical Fourier research, this summary idea creates a origin for loads of smooth research, and it includes a variety of based effects and methods which are of curiosity of their personal correct.
This booklet develops the summary thought in addition to a well-chosen collection of concrete examples that exemplify the implications and convey the breadth in their applicability. After a initial bankruptcy containing the required heritage fabric on Banach algebras and spectral concept, the textual content units out the final thought of in the neighborhood compact teams and their unitary representations, via a improvement of the extra particular conception of research on Abelian teams and compact teams. there's an in depth bankruptcy at the concept of brought on representations and its functions, and the e-book concludes with a extra casual exposition at the concept 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 basic facts of a limited type of Wiener’s theorem
- Explains the relation among SU(2) and SO(3) by way of quaternions, a chic process that brings SO(4) into the image with little effort
- Discusses representations of the discrete Heisenberg team and its principal quotients, illustrating the Mackey laptop 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, offering the necessities of harmonic research on in the community compact teams in a concise and obtainable form.
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