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A contribution to group representations in locally convex spaces

โœ Scribed by J. P. Jurzak

Publisher
Springer
Year
1977
Tongue
English
Weight
344 KB
Volume
1
Category
Article
ISSN
0377-9017

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โœฆ Synopsis

Let U be a continuous representation of a (connected) locally compact group G in a separated locally convex space E. It is shown that the study of U is equivalent to the study of a family Ui of continuous representations of G in Fr6chet spaces Fi. If U is equicontinuous, the F i are Banach spaces, and the Ui are realized by isometric operators. When U is topologically irreducible, it is Na'tmark equivalent to a Fr6chet (or isometric Banach, in the equicontinuous case) continuous representation. Similar results hold for semi-groups.

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## Abstract This paper deals with the study of a mathematical model of photon transport in an interstellar cloud where a localized source is present. The source is represented by a Dirac delta functional. The problem is studied in the setting of locally convex spaces. By means of the theory of semi