Polynomially bounded solutions to the Loewner differential equation in several complex variables |
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| Authors: | H Hamada |
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| Institution: | Faculty of Engineering, Kyushu Sangyo University, 3-1 Matsukadai 2-Chome, Higashi-ku, Fukuoka 813-8503, Japan |
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| Abstract: | We determine the form of polynomially bounded solutions to the Loewner differential equation that is satisfied by univalent subordination chains of the form f(z,t)=etAz+?, where A∈L(Cn,Cn) has the property m(A)>0. Here m(A)=min{R〈A(z),z〉:‖z‖=1}. We also give sufficient conditions for g(z,t)=L(f(z,t)) to be polynomially bounded, where f(z,t) is an A-normalized polynomially bounded Loewner chain solution to the Loewner differential equation. |
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| Keywords: | Biholomorphic mapping Loewner differential equation Polynomially bounded Subordination Subordination chain |
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