Univalent functions and \(\mathrm{Diff}(S^1)/S^1\)
type: Item
instance of: scholarly article
title: Univalent functions and \(\mathrm{Diff}(S^1)/S^1\)
zbMATH Open document ID: 1255.30027
author: Simon Davis
publication date: 2012-11-07T00:00:00Z
review text: The author considers the space \(\mathcal A\) of univalent functions that are analytic in the unit disk (and apparently continuous and differentiable in the closed unit disk, but it is not stated explicitly). The paper contains two theorems. In the first theorem the author claims that there is a differentiable invertible map \(\phi_C\) from the space Diff\((S^1)/S^1\) of diffeomorphisms of the unit circle modulo rotations onto the space \(\mathcal A\). The map \(\phi_C\) is not defined in the paper. The reader is refered to two papers from the year 1987. Also, no differentiable structure is indicated on \(\mathcal A\) or on Diff\((S^1)/S^1\) . The inverse map is defined as the restriction of functions from \(\mathcal A\) to the unit circle \(S^1\), but the restriction does not take \(S^1\) to \(S^1\) in general, so the definition is not precise. The second theorem extends this result to the supersymmetric generalization \(S^{1,1}\) of \(S^1\) and to the space of superanalytic functions on \(S^{1,1}\).
reviewed by: Agnieszka Wisniowska-Wajnryb
Mathematics Subject Classification ID: 30C50
Mathematics Subject Classification ID: 30C55
Mathematics Subject Classification ID: 58C50
Mathematics Subject Classification ID: 83E30
zbMATH DE Number: 6102817
zbMATH Keywords: univalent
zbMATH Keywords: diffeomorphism group
zbMATH Keywords: superanalytic functions
MaRDI profile type: Publication
full work available at URL: s10114-011-0125-5
OpenAlex ID: W2157661676
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DOI: 10.1007/S10114-011-0125-5
published in: Acta Mathematica Sinica, English Series
description: scientific article; zbMATH DE number 6102817