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Holomorphie quaternionienne

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Abstract

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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Authors and Affiliations

  1. Faculté de Mathématiques et Informatique, Université de Picardie Jules Verne, 33, rue Saint-Leu 80039, Amiens, France

    Louis Pernas

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  1. Louis Pernas
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Correspondence to Louis Pernas.

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Pernas, L. Holomorphie quaternionienne. AACA 8, 283–298 (1998). https://doi.org/10.1007/BF03043100

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  • DOI: https://doi.org/10.1007/BF03043100

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