Browsing by Author "Abreu Blaya, Ricardo"

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Citation - WoS: 7
Citation - Scopus: 9
Boundary Value Problems for the Cimmino System Via Quaternionic Analysis
(Elsevier Science Inc, 2012) Abreu Blaya, Ricardo; Bory Reyes, Juan; Guzman Adan, Ali; Schneider, Baruch
In this paper, we study a class of boundary value problems for a first order linear partial differential equation (all of whose solutions are harmonic functions), which is called the Cimmino system. With the help of the one-to-one correspondence between the theory of quaternion valued hyperholomorphic functions and that of Cimmino system's solutions, necessary and sufficient conditions for the solvability of the non-homogeneous Cimmino system coupled by the boundary conditions are derived and its general solution is explicitly described. (C) 2012 Elsevier Inc. All rights reserved.
Citation - WoS: 4
Citation - Scopus: 4
On the Hilbert Formulas and of Change of Integration Order for Some Singular Integrals in the Unit Circle
(Scientific Technical Research Council Turkey-Tubitak, 2018) Bory Reyes, Juan; Abreu Blaya, Ricardo; Perez De La Rosa, Marco Antonio; Schneider, Baruch
We obtain some analogues of the Hilbert formulas on the unit circle for alpha-hyperholomorphic function theory when alpha is a complex number. Such formulas relate a pair of components of the boundary value of an alpha-hyperholomorphic function in the unit circle with the other one. Furthermore, the corresponding Poincare-Bertrand formula for the alpha-hyperholomorphic singular integrals in the unit circle is presented.
Citation - WoS: 5
Citation - Scopus: 4
Poincare-Bertrand and Hilbert Formulas for the Cauchy-Cimmino Singular Integrals
(Springer Basel Ag, 2017) Bory Reyes, Juan; Abreu Blaya, Ricardo; Antonio Perez-de la Rosa, Marco; Schneider, Baruch
The Cimmino system offers a natural and elegant generalization to four-dimensional case of the Cauchy-Riemann system of first order complex partial differential equations. Recently, it has been proved that many facts from the holomorphic function theory have their extensions onto the Cimmino system theory. In the present work a Poincar,-Bertrand formula related to the Cauchy-Cimmino singular integrals over piecewise Lyapunov surfaces in is derived with recourse to arguments involving quaternionic analysis. Furthermore, this paper obtains some analogues of the Hilbert formulas on the unit 3-sphere and on the 3-dimensional space for the theory of Cimmino system.
Poincare-Bertrand and Hilbert Formulas for the Cauchy-Cimmino Singular Integrals (vol 27, Pg 2933, 2017)
(Springer Basel Ag, 2019) Bory Reyes, Juan; Abreu Blaya, Ricardo; Antonio Perez-de la Rosa, Marco; Schneider, Baruch
[Abstract Not Available]