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 sleek research, and it encompasses a variety of based effects and strategies which are of curiosity of their personal correct.
This ebook develops the summary conception besides a well-chosen choice of concrete examples that exemplify the consequences and express the breadth in their applicability. After a initial bankruptcy containing the mandatory history fabric on Banach algebras and spectral concept, the textual content units out the final conception of in the neighborhood compact teams and their unitary representations, via a improvement of the extra particular thought of research on Abelian teams and compact teams. there's an intensive bankruptcy at the idea of triggered representations and its functions, and the publication concludes with a extra casual exposition at the idea of representations of non-Abelian, non-compact groups.
Featuring large updates and new examples, the Second Edition:
- Adds a brief part on von Neumann algebras
- Includes Mark Kac’s easy evidence of a constrained kind of Wiener’s theorem
- Explains the relation among SU(2) and SO(3) by way of quaternions, a chic procedure that brings SO(4) into the image with little effort
- Discusses representations of the discrete Heisenberg staff and its relevant 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, offering the necessities of harmonic research on in the community compact teams in a concise and obtainable form.
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A Course in Abstract Harmonic Analysis, Second Edition (Textbooks in Mathematics) by Gerald B. Folland