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The analogue of the Riesz-Dunford functional calculus has been introduced and studied recently as well as the theory of semigroups and groups of linear quaternionic operators. In this paper we suppose that T is the infinitesimal generator of a strongly continuous group of operators (ZT (t))t2R and we show how we can define bounded operators f(T ), where f belongs to a class of functions which is larger than the class of slice regular functions, using the quaternionic Laplace-Stieltjes transform. This class will include functions that are slice regular on the S-spectrum of T but not necessarily at infinity. Moreover, we establish the relation of f(T ) with the quaternionic functional calculus and we study the problem of finding the inverse of f(T ).


This is a pre-copy-editing, author-produced PDF of an article accepted for publication in Analysis and Applications , volume 15, in 2017 following peer review. The definitive publisher-authenticated version is available online at DOI: 10.1142/S021953051650007X

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World Scientific



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