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The paper deals with several aspects of Fueter-holomorphic functions. In the first part a Cauchy-type formula as well as a Morera-type theorem are proved. The second part is concerned with “hemiharmonic” functions which are solutions of δ2 f = 0 and are closely related to holomorphic functions. They satisfy a “Mean value” theorem. In the third part new characterizations of holomorphy are given. The fourth part is a study of homogeneous hemiharmonic and holomorphic functions.
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