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Author Efraimidis, I.; Ferrada-Salas, A.; Hernandez, R.; Vargas, R.
Title Schwarzian derivatives for pluriharmonic mappings Type
Year 2021 Publication Journal of Mathematical Analysis and Applications Abbreviated Journal J. Math. Anal. Appl.
Volume 495 Issue 1 Pages 124716
Keywords Pluriharmonic mapping; Pre-Schwarzian derivative; Schwarzian derivative
Abstract A pre-Schwarzian and a Schwarzian derivative for locally univalent pluriharmonic mappings in Cn are introduced. Basic properties such as the chain rule, multiplicative invariance and affine invariance are proved for these operators. It is shown that the pre-Schwarzian is stable only with respect to rotations of the identity. A characterization is given for the case when the pre-Schwarzian derivative is holomorphic. Furthermore, it is shown that if the Schwarzian derivative of a pluriharmonic mapping vanishes then the analytic part of this mapping is a Mobius transformation. Some observations are made related to the dilatation of pluriharmonic mappings and to the dilatation of their affine transformations, revealing differences between the theories in the plane and in higher dimensions. An example is given that rules out the possibility for a shear construction theorem to hold in Cn, for n >= 2. (C) 2020 Elsevier Inc. All rights reserved.
Address
Corporate Author Thesis
Publisher Place of Publication Editor
Language Summary Language Original Title
Series Editor Series Title Abbreviated Series Title
Series Volume Series Issue Edition
ISSN 0022-247X ISBN Medium
Area Expedition Conference
Notes Approved
Call Number UAI @ alexi.delcanto @ Serial 1317
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Author Efraimidis, I.; Gaona, J.; Hernandez, R.; Venegas, O.
Title On harmonic Bloch-type mappings Type
Year 2017 Publication Complex Variables And Elliptic Equations Abbreviated Journal Complex Var. Elliptic Equ.
Volume 62 Issue 8 Pages 1081-1092
Keywords Bloch functions; harmonic functions; Jacobian; univalent functions; schlicht radius; growth estimates; coefficient estimates; 30C25; 30C50; 30D45; 30H30
Abstract Let f be a complex-valued harmonicmapping defined in the unit disk D. We introduce the following notion: we say that f is a Bloch-type function if its Jacobian satisfies This gives rise to a new class of functions which generalizes and contains the well-known analytic Bloch space. We give estimates for the schlicht radius, the growth and the coefficients of functions in this class. We establish an analogue of the theorem which, roughly speaking, states that for. analytic log. is Bloch if and only if. is univalent.
Address [Efraimidis, I.] Univ Autonoma Madrid, Dept Matemat, Madrid, Spain, Email: iason.efraimidis@uam.es
Corporate Author Thesis
Publisher Taylor & Francis Ltd Place of Publication Editor
Language English Summary Language Original Title
Series Editor Series Title Abbreviated Series Title
Series Volume Series Issue Edition
ISSN 1747-6933 ISBN Medium
Area Expedition Conference
Notes WOS:000399938900004 Approved
Call Number UAI @ eduardo.moreno @ Serial 729
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