Journal Home Page Cumulative Index List of all Volumes Complete Contentsof this Volume Previous Article Journal of Convex Analysis 18 (2011), No. 2, 367--377Copyright 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 [ Fulltext-pdf  (131  KB)] for subscribers only.