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Concepts of differentiability and analyticity on certain classes of topological groups
Published online by Cambridge University Press: 24 October 2008
Abstract
We introduce the concepts of a local seminorm on a topological group and of a locally convex group, showing that discrete groups, locally compact Abelian groups and compact groups are locally convex, and that a topological vector space is locally convex as a linear space if and only if it is locally convex as a group. We show that notions of differentiability, analyticity and derivability can be defined for locally convex groups and that these notions are suitably related and well behaved. We prove that for a locally compact Abelian group G the Fourier transforms of measures of compact support on the character group Ĝ are analytic, and for G compact the coefficients of continuous irreducible unitary representations are. Using these spaces of analytic functions we define the basic concepts of a differential geometry.
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- Research Article
- Information
- Mathematical Proceedings of the Cambridge Philosophical Society , Volume 61 , Issue 2 , April 1965 , pp. 347 - 379
- Copyright
- Copyright © Cambridge Philosophical Society 1965
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