Geodesic
TAUBERIAN THEOREMS AND SPECTRAL THEORY IN TOPOLOGICAL VECTOR SPACES
Glasgow mathematical journal, Tome 55 (2013) no. 3, pp. 511-532

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DOI

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.
DOI : 10.1017/S0017089512000699
Mots-clés : 37A30, 40E05, 43A45 
BEER, RICHARD J. DE. TAUBERIAN THEOREMS AND SPECTRAL THEORY IN TOPOLOGICAL VECTOR SPACES. Glasgow mathematical journal, Tome 55 (2013) no. 3, pp. 511-532. doi: 10.1017/S0017089512000699
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     author = {BEER, RICHARD J. DE},
     title = {TAUBERIAN {THEOREMS} {AND} {SPECTRAL} {THEORY} {IN} {TOPOLOGICAL} {VECTOR} {SPACES}},
     journal = {Glasgow mathematical journal},
     pages = {511--532},
     year = {2013},
     volume = {55},
     number = {3},
     doi = {10.1017/S0017089512000699},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089512000699/}
}
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