Coefficient body for nonlinear resolvents

Mark Elin, Fiana Jacobzon

Abstract


This paper is devoted to the study of families of so-called nonlinear resolvents. Namely, we construct polynomial transformations which map the closed unit polydisks onto the coefficient bodies for the resolvent families. As immediate applications of our results we present a covering theorem and a sharp estimate for the Schwarzian derivative at zero on the class of resolvents.

Keywords


Holomorphic function; infinitesimal generator; nonlinear resolvent; Schur parameter

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References


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DOI: http://dx.doi.org/10.17951/a.2019.73.2.45-57
Date of publication: 2020-01-16 07:29:31
Date of submission: 2020-01-09 15:21:52


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