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image/svg+xml Jakob Voss, based on art designer at PLoS, modified by Wikipedia users Nina and Beao Closed Access logo, derived from PLoS Open Access logo. This version with transparent background. http://commons.wikimedia.org/wiki/File:Closed_Access_logo_transparent.svg Jakob Voss, based on art designer at PLoS, modified by Wikipedia users Nina and Beao Israel Journal of Ma...arrow_drop_down
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Israel Journal of Mathematics
Article . 1987 . Peer-reviewed
License: Springer TDM
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image/svg+xml Jakob Voss, based on art designer at PLoS, modified by Wikipedia users Nina and Beao Closed Access logo, derived from PLoS Open Access logo. This version with transparent background. http://commons.wikimedia.org/wiki/File:Closed_Access_logo_transparent.svg Jakob Voss, based on art designer at PLoS, modified by Wikipedia users Nina and Beao
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Generalized Grunsky coefficients and inequalities

Authors: Harmelin, Reuven;

Generalized Grunsky coefficients and inequalities

Abstract

Let \(\alpha =\{\alpha_ n\}^{\infty}_{n=1}\) be a sequence of complex numbers and \[ \alpha (w)^{\ell}=(\sum^{\infty}_{n=1}\alpha_ nw^ n)^{\ell}=\sum^{\infty}_{k=1}A_{k,\ell}(\alpha)w^ k, \] \(A_{k,\ell}(\alpha)\) are the Bell polynomials. In this article the author investigates the connection between the Bell polynomials and some invariants introduced by the reviewer. These invariants are defined by the generating function \[ f'(z)/(f(z+w)- f(w))=(1/w)+\sum^{\infty}_{n=0}\phi_ n(w)z^ n, \] where \(\{\phi_ j\}^{\infty}_{j=1}\) are known to be invariant under Möbius transformation and \(\phi_ 1\) is the Schwarzian derivative multiplied by a constant. Further the author uses these investigations to improve some of the reviewer's results concerning the univalence of a meromorphic function as well as conditions for quasiconformal extension.

Keywords

Aharonov invariants, Bell polynomials, Schwarzian derivative, Möbius transformation, Extremal problems for conformal and quasiconformal mappings, variational methods, Coefficient problems for univalent and multivalent functions of one complex variable, General theory of univalent and multivalent functions of one complex variable, Bernoulli numbers, quasiconformal extension

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
3
Average
Top 10%
Average
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