Browsing by Author "Abreu Blaya, R."

Now showing 1 - 4 of 4

Citation - WoS: 2
Citation - Scopus: 6
On Cauchy Type Integrals Related To the Cimmino System of Partial Differential Equations
(Birkhauser Verlag Ag, 2014) Abreu Blaya, R.; Bory Reyes, J.; Schneider, B.
In this paper, we established a one-to-one correspondence between quaternionic hyperholomorphic functions in R-4 congruent to C-2 and solutions (pairs of complex-valued functions) for Cimmino system of partial differential equations written in complex form. This leads to a pair of Cauchy type integrals associated with Cimmino system. The topics of the paper concern theorems which cover basic properties of those Cauchy type integrals: the SokhotskiPlemelj and Plemelj-Privalov type theorems for it as well as the necessary and sufficient condition for the possibility to extend a given pair of complexvalued Holder-continuous functions from such a surface up to a solution of Cimmino system in a Jordan domain. Formulae for the square of the corresponding singular Cauchy type integrals are given. The proofs of all these facts are based on intimate relations between the theory of Cimmino system and some version of quaternionic analysis.
Citation - WoS: 4
Citation - Scopus: 1
On the 2d Quaternionic Metaharmonic Layer Potentials
(Springer Basel Ag, 2017) Bory Reyes, J.; Abreu Blaya, R.; Perez de la Rosa, M. A.; Schneider, B.
This paper aims to study several boundary value properties, to derive a Poincare-Bertrand formula and to solve some Dirichlet-type problems for the 2D quaternionic metaharmonic layer potentials.
Citation - Scopus: 2
On the Hilbert Formulas on the Unit Circle for Alpha-Hyperholomorphic Function Theory
(Taylor & Francis Ltd, 2018) Bory Reyes, J.; Abreu Blaya, R.; Perez-de la Rosa, M. A.; Schneider, B.
We obtain some analogues of the Hilbert formulas on the unit circle for alpha-hyperholomorphic function theory in R-2 for a being a complex quaternionic number. The obtained formulas relate a pair of components of the boundary value of an alpha-hyperholomorphic function in the unit discwith the other pair of components and, hence, being analogous to the case of the theory of functions of one complex variable.
Citation - WoS: 10
Citation - Scopus: 10
A Quaternionic Treatment of Inhomogeneous Cauchy-Riemann Type Systems in Some Traditional Theories
(Springer Basel Ag, 2017) Bory Reyes, J.; Abreu Blaya, R.; Perez-de la Rosa, M. A.; Schneider, B.
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 C-valued functions and we describe its general solution by embedding the system in an appropriate quaternionic setting.