Open Access
2016 Hilbert-substructure of Real Measurable Spaces on Reductive Groups, I; Basic Theory
OO Oyadare
J. Gen. Lie Theory Appl. 10(1): 1-4 (2016). DOI: 10.4172/1736-4337.1000242


This paper reconsiders the age-long problem of normed linear spaces which do not admit inner product and shows that, for some subspaces, Fn(G), of real Lp(G)−spaces (when G is a reductive group in the Harish-Chandra class and p=2n), the situation may be rectified, via an outlook which generalizes the fine structure of the Hilbert space, L2(G). This success opens the door for harmonic analysis of unitary representations, G→End(Fn(G)), of G on the Hilbert-substructure Fn(G), which has hitherto been considered impossible.


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OO Oyadare. "Hilbert-substructure of Real Measurable Spaces on Reductive Groups, I; Basic Theory." J. Gen. Lie Theory Appl. 10 (1) 1 - 4, 2016.


Published: 2016
First available in Project Euclid: 3 February 2017

zbMATH: 06685546
MathSciNet: MR3652754
Digital Object Identifier: 10.4172/1736-4337.1000242

Keywords: ‎Hilbert spaces , orthogonal polynomials , reductive groups

Rights: Copyright © 2016 Ashdin Publishing (2009-2013) / OMICS International (2014-2016)

Vol.10 • No. 1 • 2016
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