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Efraimidis, I.; Ferrada-Salas, A.; Hernandez, R.; Vargas, R. |
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Title |
Schwarzian derivatives for pluriharmonic mappings |
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2021 |
Publication |
Journal of Mathematical Analysis and Applications |
Abbreviated Journal |
J. Math. Anal. Appl. |
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Volume |
495 |
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1 |
Pages |
124716 |
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Keywords |
Pluriharmonic mapping; Pre-Schwarzian derivative; Schwarzian derivative |
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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. |
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0022-247X |
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UAI @ alexi.delcanto @ |
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1317 |
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Author |
Efraimidis, I.; Gaona, J.; Hernandez, R.; Venegas, O. |
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Title |
On harmonic Bloch-type mappings |
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Year |
2017 |
Publication |
Complex Variables And Elliptic Equations |
Abbreviated Journal |
Complex Var. Elliptic Equ. |
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62 |
Issue |
8 |
Pages |
1081-1092 |
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Keywords |
Bloch functions; harmonic functions; Jacobian; univalent functions; schlicht radius; growth estimates; coefficient estimates; 30C25; 30C50; 30D45; 30H30 |
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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. |
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[Efraimidis, I.] Univ Autonoma Madrid, Dept Matemat, Madrid, Spain, Email: iason.efraimidis@uam.es |
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Taylor & Francis Ltd |
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English |
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1747-6933 |
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WOS:000399938900004 |
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UAI @ eduardo.moreno @ |
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729 |
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