A functional calculus is a construction which associates with an
operator or a family of operators a homomorphism from a function
space into a subspace of continuous linear operators, i.e. a method
for defining "functions of an operator". Perhaps the most familiar
example is based on the spectral theorem for bounded self-adjoint
operators on a complex Hilbert space.This book contains an
exposition of several such functional calculi. In particular, there
is an exposition based on the spectral theorem for bounded,
self-adjoint operators, an extension to the case of several
commuting self-adjoint operators and an extension to normal
operators. The Riesz operational calculus based on the Cauchy
integral theorem from complex analysis is also described. Finally,
an exposition of a functional calculus due to H. Weyl is given.
General
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