Functional calculus for non-commuting operators with real spectra via an iterated Cauchy formula

Details Functional calculus for non-commuting operators with real spectra via an iterated Cauchy formula Functional calculus for non-commuting operators with real spectra via an iterated Cauchy formula

2003-03-03

arxiv.org/abs/math/0303024v1

Mathematics

Spectral Theory

Scientific paper

We define a smooth functional calculus for a non-commuting tuple of
(unbounded) operators $A_j$ on a Banach space with real spectra and resolvents
with temperate growth, by means of an iterated Cauchy formula. The construction
is also extended to tuples of more general operators allowing smooth functional
calculii. We also discuss the relation to the case with commuting operators.

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