Projective analytic vectors and infinitesimal generators |
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Authors: | Rodrigo A. H. M. Cabral |
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Affiliation: | Mathematics Department, Institute of Mathematics and Statistics, University of São Paulo (IME-USP), São Paulo, SP, Brazil |
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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. |
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Keywords: | analytic vector locally convex space one-parameter group projective limit pseudodifferential operator |
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