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“…There exists another conventional function theory to be considered. This is the case of the Cimmino system, which was introduced in 1941 by G. Cimmino [10] and recently researchers, following [35], have come to understand several aspects of the system, see [1,2,6,8,9,11,37,38]. The next step to our work would be to develop of Bergman spaces theory induced by the Cimmino system, whose solutions form a proper subset of the π 2 −hyperholomorphic functions class.…”

confidence: 99%

“…There exists another conventional function theory to be considered. This is the case of the Cimmino system, which was introduced in 1941 by G. Cimmino [10] and recently researchers, following [35], have come to understand several aspects of the system, see [1,2,6,8,9,11,37,38]. The next step to our work would be to develop of Bergman spaces theory induced by the Cimmino system, whose solutions form a proper subset of the π 2 −hyperholomorphic functions class.…”

confidence: 99%

“…Remark If $f:\Omega \to \mathbb{H}$ has $u:\Omega \to \mathbb{C}$ and $v:\Omega \to \mathbb{C}$ as complex components then the ψ‐hyperholomorphicity of f can be interpreted as the following system of equations $${}^{{\psi}_{\theta}}D\left[f\right]=0\iff \left\{\begin{array}{c}right{\partial}_{{\overline{z}}_{1}}u-{e}_{1}{e}^{{e}_{1}\theta}\xb7{\partial}_{{z}_{2}}\overline{v}=0,\\ right{e}_{1}{e}^{-{e}_{1}\theta}\xb7{\partial}_{{\overline{z}}_{2}}u-{\partial}_{{z}_{1}}\overline{v}=0.\end{array}\right.$$ The system above may be interpreted as a generalization of that study by the distinguished Italian mathematician Gianfranco Cimmino (12 Marzo 1908–30 Mayo 1989), which can be recovered from if we take $\theta =\frac{\pi}{2}$. In an in‐depth study of Cimmino system using quaternionic analysis has been presented. As the basic for the development of our theory, we need to point out that the class of all equivalent structural sets defines the same hyperholomorphicity, then we should in fact further restrict our analysis to consider only structural sets not to be equivalent from the same side of hyperholomorphicity we are assumed. …”

confidence: 99%

“…The system above may be interpreted as a generalization of that study by the distinguished Italian mathematician Gianfranco Cimmino (12 Marzo 1908-30 Mayo 1989, which can be recovered from (3.2) if we take θ = π 2 . In [1] an in-depth study of Cimmino system using quaternionic analysis has been presented.…”

confidence: 99%

“…In the same paper the Authors address the problem whether conditions (3) are also su cient for the resolubility of the Dirichlet problem (2). More recently, Abreu Blaya et al [1] studied (1) by means of quaternionic analysis. In particular, they found some di↵erent necessary and su cient conditions involving some particular integral operators.…”

confidence: 99%