By Gerald B. Folland
A direction 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 thought creates a starting place for loads of sleek research, and it features a variety of based effects and strategies which are of curiosity of their personal correct.
This booklet develops the summary idea in addition to a well-chosen collection of concrete examples that exemplify the implications and express the breadth in their applicability. After a initial bankruptcy containing the required historical past fabric on Banach algebras and spectral conception, the textual content units out the overall conception of in the neighborhood compact teams and their unitary representations, by way of a improvement of the extra particular thought of research on Abelian teams and compact teams. there's an intensive bankruptcy at the concept of precipitated representations and its functions, and the publication concludes with a extra casual exposition at the concept of representations of non-Abelian, non-compact groups.
Featuring broad updates and new examples, the Second Edition:
- Adds a quick 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) when it comes to quaternions, a sublime technique that brings SO(4) into the image with little effort
- Discusses representations of the discrete Heisenberg team and its crucial quotients, illustrating the Mackey computer 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, 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