Projective Analytic Vectors and Infinitesimal Generators
Abstract
We establish the notion of a ``projective analytic vector'', whose defining requirements are weaker than the usual ones of an analytic vector, and use it to prove generation theorems for one-parameter groups on locally convex spaces. More specifically, we give a characterization of the generators of strongly continuous one-parameter groups which arise as the result of a projective limit procedure, in which the existence of a dense set of projective analytic vectors plays a central role. An application to strongly continuous Lie group representations on Banach spaces is given, with a focused analysis on concrete algebras of functions and of pseudodifferential operators.
Cite
@article{arxiv.1911.05851,
title = {Projective Analytic Vectors and Infinitesimal Generators},
author = {Rodrigo A. H. M. Cabral},
journal= {arXiv preprint arXiv:1911.05851},
year = {2023}
}
Comments
20 pages. Final version published in Mathematische Nachrichten. This work investigates in more depth the concept of a projective analytic vector, which has first appeared in arXiv:1906.07931v3. arXiv admin note: text overlap with arXiv:1906.07931