By Gerald B. Folland
A path in summary Harmonic Analysis is an creation 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 concept creates a origin for loads of glossy research, and it encompasses a variety of dependent effects and strategies which are of curiosity of their personal correct.
This e-book develops the summary idea in addition to a well-chosen choice 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 final thought of in the neighborhood compact teams and their unitary representations, through a improvement of the extra particular conception of study on Abelian teams and compact teams. there's an intensive bankruptcy at the conception of caused representations and its functions, and the booklet concludes with a extra casual exposition at the concept 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 basic evidence of a limited kind 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 computer 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 neighborhood compact teams in a concise and obtainable form.
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Additional 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