TY - JOUR
T1 - On the Slice Regular Schwarz Derivative
AU - González-Cervantes, J. Oscar
N1 - Publisher Copyright:
© 2019, Springer Nature Switzerland AG.
PY - 2019/9/1
Y1 - 2019/9/1
N2 - The aim of this paper is to introduce, in the context of slice regular functions, three notions of the quaternionic Schwarz derivative with their the basic properties: the characterization of zeros, the conformal covariant property and the conformal invariant property. These concepts mimic the structure of the complex Schwarz derivative which is a differential operator with several properties and applications. Particularly, one of these operators is curiously related to the generalization of the schwarzian derivative over vector spaces given by Ryan (Ann Pol Math 57:29–44, 1992).
AB - The aim of this paper is to introduce, in the context of slice regular functions, three notions of the quaternionic Schwarz derivative with their the basic properties: the characterization of zeros, the conformal covariant property and the conformal invariant property. These concepts mimic the structure of the complex Schwarz derivative which is a differential operator with several properties and applications. Particularly, one of these operators is curiously related to the generalization of the schwarzian derivative over vector spaces given by Ryan (Ann Pol Math 57:29–44, 1992).
KW - Schwarz derivative
KW - Slice regular function
UR - http://www.scopus.com/inward/record.url?scp=85071226799&partnerID=8YFLogxK
U2 - 10.1007/s00006-019-1004-x
DO - 10.1007/s00006-019-1004-x
M3 - Artículo
AN - SCOPUS:85071226799
SN - 0188-7009
VL - 29
JO - Advances in Applied Clifford Algebras
JF - Advances in Applied Clifford Algebras
IS - 4
M1 - 82
ER -