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Contractive polynomials of the Volterra operator

Volume 240 / 2018

A.F.M. ter Elst, Jaroslav Zemánek Studia Mathematica 240 (2018), 201-211 MSC: Primary 47B38; Secondary 47B44, 47G10. DOI: 10.4064/sm8051-5-2017 Published online: 12 October 2017

Abstract

If $\varphi $ is a holomorphic function with $\varphi (0) = 1$ then we present sufficient conditions and necessary conditions for $\varphi (V)$ to be a contraction, where $V$ is the Volterra operator on $L_2(0,1)$. In particular we show that this may happen for certain polynomials $\varphi $, disproving a conjecture by Lyubich and Tsedenbayar.

Authors

  • A.F.M. ter ElstDepartment of Mathematics
    University of Auckland
    Private bag 92019
    Auckland 1142, New Zealand
  • Jaroslav ZemánekInstitute of Mathematics
    Polish Academy of Sciences
    Śniadeckich 8
    00-656 Warszawa, Poland

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