LOEWNER PDE IN INFINITE DIMENSIONS

作     者：Graham, Ian Hamada, Hidetaka Kohr, Gabriela Kohr, Mirela 

作者机构：Department of Mathematics University of Toronto TorontoONM5S 2E4 Canada Faculty of Science and Engineering Kyushu Sangyo University 3-1 Matsukadai 2-Chome Higashi-ku Fukuoka813-8503 Japan Faculty of Mathematics and Computer Science Babeş-Bolyai University 1 M. Kogal- niceanu Str. Cluj-Napoca400084 Romania 

出 版 物：《arXiv》 (arXiv)

年 卷 期：2023年

核心收录：

主　　题：Banach spaces 

摘      要：In this paper, we prove the existence and uniqueness of the solution f(z, t) of the Loewner PDE with normalization Df(0, t) = etA, where A ∈ L(X, X) is such that k+(A) e−(t−s)A for t ≥ s ≥ 0, where m(A) 0, which satisfy the semigroup property on the unit ball of a complex Banach space X. We further obtain the biholomorphicity of A-normalized univalent subordination chains under some normality condition on the unit ball of a reflexive complex Banach space X. We prove the existence of the biholomorphic solutions f(z, t) of the Loewner PDE with normalization Df(0, t) = etA on the unit ball of a separable reflexive complex Banach space X. The results obtained in this paper give some positive answers to the open problems and conjectures proposed by the authors in 2013. Copyright © 2023, The Authors. All rights reserved.