Spectrum as the Support of Functional Calculus

Details Spectrum as the Support of Functional Calculus Spectrum as the Support of Functional Calculus

2002-08-30

arxiv.org/abs/math/0208249v1

in Functional Analysis and its Applications (V.Kadets et al eds), Elsevier Sci. Publ., 2004, pp.133-142

Mathematics

Functional Analysis

LaTeX, pages 10 pages, 1 PS figures

Scientific paper

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.

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