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A Quaternionic Treatment of Inhomogeneous Cauchy–Riemann Type Systems in Some Traditional Theories

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Abstract

In this paper we provide a necessary and sufficient condition for the solvability of inhomogeneous Cauchy–Riemann type systems where the datum consists of continuous \({\mathbb {C}}\)-valued functions and we describe its general solution by embedding the system in an appropriate quaternionic setting.

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Acknowledgments

J. Bory Reyes and M. A. Pérez-de la Rosa were partially supported by Instituto Politécnico Nacional in the framework of SIP programs and by the Asociación Mexicana de Cultura, A. C., respectively.

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Authors and Affiliations

  1. ESIME-Zacatenco, Instituto Politécnico Nacional, CD-MX, 07738, Mexico, Mexico

    J. Bory Reyes

  2. Facultad de Informática y Matemática, Universidad de Holguín, 80100, Holguín, Cuba

    R. Abreu Blaya

  3. Departamento de Matemáticas, Instituto Tecnológico Autónomo de México, Rio Hondo #1, Col. Progreso Tizapán, 01080, Mexico, DF, Mexico

    M. A. Pérez-de la Rosa

  4. Faculty of Sciences and Literature, Department of Mathematics, Izmir University of Economics, 35330, Izmir, Turkey

    B. Schneider

Authors
  1. J. Bory Reyes
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  2. R. Abreu Blaya
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  3. M. A. Pérez-de la Rosa
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  4. B. Schneider
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Corresponding author

Correspondence to B. Schneider.

Additional information

Communicated by Fabrizio Colombo.

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Reyes, J.B., Blaya, R.A., la Rosa, M.A.Pd. et al. A Quaternionic Treatment of Inhomogeneous Cauchy–Riemann Type Systems in Some Traditional Theories. Complex Anal. Oper. Theory 11, 1017–1034 (2017). https://doi.org/10.1007/s11785-016-0608-6

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