Journal of Convex Analysis 18 (2011), No. 2, 367--377
Copyright Heldermann Verlag 2011
Legendre-Fenchel Transform of the Spectral Exponent of Analytic Functions of Weighted Composition Operators
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
[Abstract-pdf]
Let $f$ be an analytic function with nonnegative coefficients. We derive the Legendre-Fenchel transform of the composition $\ln \circ f \circ \exp$ as a function depending on coefficients of $f$. 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.
Keywords: Weighted composition operators, spectral radius, Legendre-Fenchel transform.
MSC: 47A10, 47B37, 44A15
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