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TAUBERIAN THEOREMS AND SPECTRAL THEORY IN TOPOLOGICAL VECTOR SPACES

Published online by Cambridge University Press:  25 February 2013

RICHARD J. DE BEER
Affiliation:
Internal Box 209, School of Computer, Statistics & Mathematical Sciences North-West University(Potchefstroom Campus) Pvt. Bag X6001, Potchefstroom 2520, South Africa e-mail: richardjohndebeer@gmail.com
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Abstract

We investigate the spectral theory of integrable actions of a locally compact abelian group on a locally convex vector space. We start with an analysis of various spectral subspaces induced by the action of the group. This is applied to analyse the spectral theory of operators on the space, generated by measures on the group. We apply these results to derive general Tauberian theorems that apply to arbitrary locally compact abelian groups acting on a large class of locally convex vector spaces, which includes Fréchet spaces. We show how these theorems simplify the derivation of Mean Ergodic theorems.

Type
Research Article
Copyright
Copyright © Glasgow Mathematical Journal Trust 2013 

References

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