Abstract

Let ff be an analytic function with nonnegative coefficients. We derive the Legendre-Fenchel transform of the composition ln⁡∘f∘exp⁡\ln \circ f \circ \exp as a function depending on coefficients of ff. We apply it to obtain the variational principle for the spectral exponent of operators that can be written as analytic functions of the weighted composition operators.

Author information

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Urszula Ostaszewska

Institute of Mathematics, University of Bialystok, Akademicka 2, 15-267 Bialystok, Poland

uostasze@math.uwb.edu.pl

Krzysztof Zajkowski

Institute of Mathematics, University of Bialystok, Akademicka 2, 15-267 Bialystok, Poland

kryza@math.uwb.edu.pl

Keywords

  • Weighted composition operators
  • spectral radius
  • Legendre-Fenchel transform

Mathematics Subject Classification

47A10, 47B37, 44A15

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Suggested citation

U. Ostaszewska, K. Zajkowski. “Legendre-Fenchel Transform of the Spectral Exponent of Analytic Functions of Weighted Composition Operators.” Journal of Convex Analysis 18 (2011), No. 2, 367–377. https://doi.org/10.68381/jca18020

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Published by Heldermann Verlag, 2011. Rights now held by Banach Press LLC.