On some structural sets and a quaternionic ‐hyperholomorphic function theory |
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| Authors: | Ricardo Abreu Blaya Juan Bory Reyes Alí Guzmán Adán Uwe Kaehler |
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| Affiliation: | 1. Facultad de Informática y Matemática, Universidad de Holguín, Holguín, Cuba;2. ESIME‐Zacatenco, Instituto Politécnico Nacional, México, DF 07738, México;3. Departamento de Matemática, Universidad de Oriente, Santiago de Cuba, Cuba;4. Departamento de Matemática, Universidade de Aveiro, Aveiro, Portugal |
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| Abstract: | Quaternionic analysis is regarded as a broadly accepted branch of classical analysis referring to many different types of extensions of the Cauchy‐Riemann equations to the quaternion skew field  . It relies heavily on results on functions defined on domains in  or  with values in  . This theory is centred around the concept of ψ‐hyperholomorphic functions related to a so‐called structural set ψ of  or  respectively. The main goal of this paper is to develop the nucleus of the  ‐hyperholomorphic function theory, i.e., simultaneous null solutions of two Cauchy‐Riemann operators associated to a pair  of structural sets of  . Following a matrix approach, a generalized Borel‐Pompeiu formula and the corresponding Plemelj‐Sokhotzki formulae are established. |
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| Keywords: | Quaternionic analysis Structural sets Cauchy‐Riemann operator 30G35 |
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