Product Description
The theme of this book is the Structure Theory of compact groups. It contains a completely self-contained introduction to linear Lie groups and a substantial body of material on compact Lie groups. The authors' approach is distinctive in so far as they define a linear Lie group as a particular subgroup of the multiplicative group of a Banach algebra. Compact Lie groups are recognized at an early stage as being linear Lie groups. This approach avoids the use of machinery on manifolds.

The text is written in a style to make it accessible to the beginning graduate student with a basic knowledge in analysis, algebra, and topology. At the same time the expert will find it an excellent and rich source of information on the general structure theory of compact groups. ... Read more

Product Description

From the reviews: "..., the book must be of great help for a researcher who already has some idea of Lie theory, wants to employ it in his everyday research and/or teaching, and needs a source for customary reference on the subject. From my viewpoint, the volume is perfectly fit to serve as such a source, ... On the whole, it is quite a pleasure, after making yourself comfortable in that favourite office armchair of yours, just to keep the volume gently in your hands and browse it slowly and thoughtfully; and after all, what more on Earth can one expect of any book?" --The New Zealand Mathematical Society Newsletter

Product Description
Over 6000 reviews, which appeared in MR between 1940 and 1967, are included in this two-part volume. These reviews, with an author index, are arranged under 290 subject headings, and appear in their entirety. ... Read more

Product Description
Chapters: Pontryagin Duality. Source: Wikipedia. Pages: 156. Not illustrated. Free updates online. Purchase includes a free trial membership in the publisher's book club where you can select from more than a million books without charge. Excerpt: In mathematics, in particular in harmonic analysis and the theory of topological groups, Pontryagin duality explains the general properties of the Fourier transform. It places in a unified context a number of observations about functions on the real line or on finite abelian groups: The theory, introduced by Lev Pontryagin and combined with Haar measure introduced by John von Neumann, André Weil and others depends on the theory of the dual group of a locally compact abelian group. It is analogous to the dual vector space of a finite-dimensional vector space: a vector space V and its dual vector space are not naturally isomorphic, but their endomorphism algebra (matrix algebras) are: via the transpose. Similarly, a group G and its dual group are not in general isomorphic, but their group algebras are: via the Fourier transform, though one must carefully define these algebras analytically. More categorically, this is not just an isomorphism of endomorphism algebras, but an isomorphism of categories see categorical considerations. A topological group is locally compact if and only if the identity e of the group has a compact neighborhood. This means that there is some open set V containing e whose closure is compact in the topology of G. One of the most remarkable facts about a locally compact group G is that it carries an essentially unique natural measure, the Haar measure, which allows one to consistently measure the "size" of sufficiently regular subsets of G. "Sufficiently regular subset" here means a Borel set; that is, an element of the -algebra generated by the compact sets. More precisely, a right Haar measure on a locally compact group G is a countably additive measure define...More: http://booksllc.net/?id=366136 ... Read more