无穷维度中的 Loewner PDE

IF 0.6 4区 数学 Q3 MATHEMATICS
Ian Graham, Hidetaka Hamada, Gabriela Kohr, Mirela Kohr
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引用次数: 0

摘要

在本文中,我们证明了在可分离的反射复巴纳赫空间 X 的单位球上,具有归一化 \(Df(0,t)=e^{tA}\) 的 Loewner PDE 的解 f(z, t) 的存在性和唯一性,其中 \(A\in L(X,X)\) 是这样的 \(k_+(A)<2m(A)\) 。特别地,我们得到了单等价施瓦茨映射 v(z,s,t)在复巴纳赫空间 X 的单位球上满足半群性质的归一化 \(Dv(0,s,t)=e^{-(t-s)A}\) for \(t\ge s\ge 0\), where \(m(A)>0\) 的双全非性。我们进一步得到了在可分离的反身复巴纳赫空间 X 的单位球上,在一些规范性条件下 A 规范化的单价隶属链的双全态性。我们证明了在可分离的反身复巴纳赫空间 X 的单位球上,具有规范化 \(Df(0,t)=e^{tA}\) 的 Loewner PDE 的双全态解 f(z, t) 的存在性。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Loewner PDE in Infinite Dimensions

In this paper, we prove the existence and uniqueness of the solution f(zt) of the Loewner PDE with normalization \(Df(0,t)=e^{tA}\), where \(A\in L(X,X)\) is such that \(k_+(A)<2m(A)\), on the unit ball of a separable reflexive complex Banach space X. In particular, we obtain the biholomorphicity of the univalent Schwarz mappings v(zst) with normalization \(Dv(0,s,t)=e^{-(t-s)A}\) for \(t\ge s\ge 0\), 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(zt) of the Loewner PDE with normalization \(Df(0,t)=e^{tA}\) 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.

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来源期刊
Computational Methods and Function Theory
Computational Methods and Function Theory MATHEMATICS, APPLIED-MATHEMATICS
CiteScore
3.20
自引率
0.00%
发文量
44
审稿时长
>12 weeks
期刊介绍: CMFT is an international mathematics journal which publishes carefully selected original research papers in complex analysis (in a broad sense), and on applications or computational methods related to complex analysis. Survey articles of high standard and current interest can be considered for publication as well.
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