Abstract.
In a previous paper we introduced the concept of a two-dimensional directional derivative of a quaternionic function along a two-dimensional plane. In this paper we provide a deeper analysis of its properties, as well as of its relations with hyperholomorphic functions, with holomorphic maps of two complex variables and with Cullen-regular functions.
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This paper is dedicated to the memory of our friend and colleague Jarolim Bureš
M. E. Luna-Elizarrarás, M. Shapiro: The research was partially supported by CONACYT projects as well as by Instituto Politécnico Nacional in the framework of COFAA and SIP programs.
M. A. Macías-Cedeño: The research was supported by Instituto Tecnológico y de Estudios Superiores de Monterrey.
Received: October, 2007. Accepted: February, 2008.
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Luna-Elizarrarás, M.E., Macías-Cedeño, M.A. & Shapiro, M. On the Derivatives of Quaternionic Functions Along Two-Dimensional Planes. AACA 19, 375–390 (2009). https://doi.org/10.1007/s00006-009-0165-4
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DOI: https://doi.org/10.1007/s00006-009-0165-4