  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.
