
Journal of Convex Analysis 18 (2011), No. 2, 367377 Copyright Heldermann Verlag 2011 LegendreFenchel Transform of the Spectral Exponent of Analytic Functions of Weighted Composition Operators Urszula Ostaszewska Institute of Mathematics, University of Bialystok, Akademicka 2, 15267 Bialystok, Poland uostasze@math.uwb.edu.pl Krzysztof Zajkowski Institute of Mathematics, University of Bialystok, Akademicka 2, 15267 Bialystok, Poland kryza@math.uwb.edu.pl [Abstractpdf] Let $f$ be an analytic function with nonnegative coefficients. We derive the LegendreFenchel 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, LegendreFenchel transform. MSC: 47A10, 47B37, 44A15 [ Fulltextpdf (131 KB)] for subscribers only. 