2002/08/30 by Vladimir V. Kisil
Mathematics · #math.FA #math.RT #msc:47A60 #msc:46H30
published as in Functional Analysis and its Applications (V.Kadets et al eds), Elsevier Sci. Publ., 2004, pp.133-142 · LaTeX, pages 10 pages, 1 PS figures
arxiv created 2002/08/30 · arxiv updated 2009/11/30
We investigate the new definition of analytic functional calculus in the terms of representation theory of SL2(R). We avoid any usage of its algebraic homomorphism property and replace it by the demand to be an intertwining operator. The related notion of spectrum and spectral mapping theorem are given. The construction is illustrated by a simple example of calculus and spectrum of non-normal n x n matrix. Keywords: Functional calculus, spectrum, intertwining operator, spectral mapping theorem, jet spaces.