On Some Properties of the Quaternionic Functional Calculus |
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Authors: | Fabrizio Colombo Irene Sabadini |
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Institution: | (1) Dipartimento di Matematica, Politecnico di Milano, Via E. Bonardi, 9, 20133 Milano, Italy |
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Abstract: | In some recent works we have developed a new functional calculus for bounded and unbounded quaternionic operators acting on
a quaternionic Banach space. That functional calculus is based on the theory of slice regular functions and on a Cauchy formula
which holds for particular domains where the admissible functions have power series expansions. In this paper, we use a new
version of the Cauchy formula with slice regular kernel to extend the validity of the quaternionic functional calculus to
functions defined on more general domains. Moreover, we show some of the algebraic properties of the quaternionic functional
calculus such as the S-spectral radius theorem and the S-spectral mapping theorem. Our functional calculus is also a natural tool to define the semigroup e
tA
when A is a linear quaternionic operator.
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Keywords: | Slice regular functions Functional calculus Spectral theory Algebraic properties S-spectral radius theorem S-spectral mapping theorem Semigroup of a linear quaternionic operator |
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