Functional Analysis

Download A Course in Abstract Harmonic Analysis, Second Edition by Gerald B. Folland PDF

By Gerald B. Folland

A path 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 conception 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 besides a well-chosen choice of concrete examples that exemplify the implications and convey the breadth in their applicability. After a initial bankruptcy containing the mandatory historical past fabric on Banach algebras and spectral conception, the textual content units out the overall thought of in the community 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 idea of brought about representations and its purposes, and the ebook concludes with a extra casual exposition at the idea of representations of non-Abelian, non-compact groups.

Featuring broad 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) by way of quaternions, a sublime procedure that brings SO(4) into the image with little effort

  • Discusses representations of the discrete Heisenberg crew and its important quotients, illustrating the Mackey computing device for normal semi-direct items and the pathological phenomena for nonregular ones

A path in summary Harmonic research, moment variation 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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