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Moscow Mathematical Journal

Volume 14, Issue 3, July–September 2014  pp. 473–489.

Some Integral Representations of Slice Hyperholomorphic Functions

Authors:  F. Colombo (1), J. O. González-Cervantes (2), and I. Sabadini (1)
Author institution:(1) Politecnico di Milano, Dipartimento di Matematica, Via E. Bonardi, 9, 20133 Milano, Italy
(2) Departamento de Matemáticas, E.S.F.M. del I.P.N. 07338, México D.F., México


In this paper we prove the analog of the Schwarz integral formula as well as other integral representations for slice monogenic functions. The key tool to establish these formulas is a suitable decomposition of slice monogenic functions. All the results that are stated in the case of slice monogenic functions hold also for slice regular functions of a quaternionic variable.

2010 Mathematics Subject Classification. 30G35.

Keywords: Slice monogenic functions, Schwarz integral formula, Harnack inequalities.

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