TY - JOUR
T1 - Poincaré–Bertrand and Hilbert formulas for the Cauchy–Cimmino singular integrals
AU - Bory Reyes, Juan
AU - Abreu Blaya, Ricardo
AU - Pérez-de la Rosa, Marco Antonio
AU - Schneider, Baruch
N1 - Publisher Copyright:
© 2017, Springer International Publishing AG.
PY - 2017/12/1
Y1 - 2017/12/1
N2 - 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 Poincaré–Bertrand formula related to the Cauchy–Cimmino singular integrals over piecewise Lyapunov surfaces in R4 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.
AB - 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 Poincaré–Bertrand formula related to the Cauchy–Cimmino singular integrals over piecewise Lyapunov surfaces in R4 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.
KW - Cimmino system
KW - Hilbert formulas
KW - Poincaré–Bertrand formula
KW - Quaternionic analysis
UR - http://www.scopus.com/inward/record.url?scp=85028847223&partnerID=8YFLogxK
U2 - 10.1007/s00006-017-0809-8
DO - 10.1007/s00006-017-0809-8
M3 - Artículo
SN - 0188-7009
VL - 27
SP - 2933
EP - 2960
JO - Advances in Applied Clifford Algebras
JF - Advances in Applied Clifford Algebras
IS - 4
ER -