By Gerald B. Folland
A direction in summary Harmonic Analysis is an advent to that a part of research on in the community compact teams that may be performed with minimum assumptions at the nature of the crowd. As a generalization of classical Fourier research, this summary thought creates a beginning for loads of sleek research, and it features a variety of dependent effects and methods which are of curiosity of their personal correct.
This ebook develops the summary thought in addition to a well-chosen number of concrete examples that exemplify the implications and express the breadth in their applicability. After a initial bankruptcy containing the required history fabric on Banach algebras and spectral concept, the textual content units out the overall idea of in the neighborhood compact teams and their unitary representations, by way of a improvement of the extra particular idea of research on Abelian teams and compact teams. there's an in depth bankruptcy at the thought of triggered representations and its purposes, and the e-book concludes with a extra casual exposition at the thought of representations of non-Abelian, non-compact groups.
Featuring large updates and new examples, the Second Edition:
- Adds a quick part on von Neumann algebras
- Includes Mark Kac’s easy facts of a constrained kind of Wiener’s theorem
- Explains the relation among SU(2) and SO(3) when it comes to quaternions, a chic process that brings SO(4) into the image with little effort
- Discusses representations of the discrete Heisenberg workforce and its relevant quotients, illustrating the Mackey desktop for normal semi-direct items and the pathological phenomena for nonregular ones
A path in summary Harmonic research, moment version serves as an entrée to complicated arithmetic, proposing the necessities of harmonic research on in the community compact teams in a concise and available form.
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Extra info 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