## Abstract

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

Original language | English |
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Pages (from-to) | 279-311 |

Number of pages | 33 |

Journal | Analysis and Applications |

Volume | 15 |

Issue number | 2 |

DOIs | |

State | Published - 1 Mar 2017 |

## Keywords

- functions of the infinitesimal generator
- quaternionic functional calculus
- Quaternionic infinitesimal generators
- quaternionic Laplace-Stieltjes transform
- S-resolvent operator
- S-spectrum

## ASJC Scopus subject areas

- Analysis
- Applied Mathematics