An application of self-conjugate differential forms to the Dirichlet problem for Cimmino system

Caramuta, P.; Cialdea, Alberto

doi:10.1080/17476933.2016.1253070

Cited by 4 publications

(1 citation statement)

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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.…”

Section: Discussionmentioning

confidence: 99%

On hyperholomorphic Bergman type spaces in domains of $\mathbb C^2$

González-Cervantes¹,

Reyes²

2021

Preprint

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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 H.In this work we deals with a well-known (θ, u)−hyperholomorphic H−valued functions class related to elements of the kernel of the Helmholtz operator with a parameter u ∈ H, just in the same way as the usual quaternionic analysis is related to the set of the harmonic functions.Given a domain Ω ⊂ H ∼ = C 2 , we define and study a Bergman spaces theory for (θ, u)− hyperholomorphic quaternion-valued functions introduced as elements of the kernel of θ u D[f ] = θ D[f ] + uf with u ∈ H defined in C 1 (Ω, H), where

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