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Harmonic Analysis of a Class of Reproducing Kernel Hilbert Spaces Arising from Groups
Contemporary Mathematics
  • Palle E.T. Jorgensen
  • Steen Pedersen, Wright State University - Main Campus
  • Feng Tian, Wright State University - Main Campus
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We study two extension problems, and their interconnections: (i) extension of positive definite continuous functions defined on subsets in locally compact groups G; and (ii) (in case of Lie groups G) representations of the associated Lie algebras La (G), i.e., representations of La (G) by unbounded skew-Hermitian operators acting in a reproducing kernel Hilbert space H-F (RKHS). Our analysis is non-trivial even if G = R-n, and even if n = 1. If G = R-n, (ii), we are concerned with finding systems of strongly commuting selfadjoint operators {T-i} extending a system of commuting Hermitian operators with common dense domain in H-F. Our general results include non-compact and non-Abelian Lie groups, where the study of unitary representations in H-F is subtle.

Presented at the AMS Special Session on Harmonic Analysis and its Applications at the Spring Eastern Sectional Meeting, Baltimore, MD, March 29-30, 2014.

Citation Information
Palle E.T. Jorgensen, Steen Pedersen and Feng Tian. "Harmonic Analysis of a Class of Reproducing Kernel Hilbert Spaces Arising from Groups" Contemporary Mathematics Vol. 650 (2015) p. 157 - 197 ISSN: 02714132
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