Geodesic
Legendre-Fenchel Transform of the Spectral Exponent of Analytic Functions of Weighted Composition Operators
Journal of convex analysis, Tome 18 (2011) no. 2, pp. 367-377

Voir la notice de l'article provenant de la source Heldermann Verlag

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.
Classification : 47A10, 47B37, 44A15
Mots-clés : Weighted composition operators, spectral radius, Legendre-Fenchel transform 
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     author = {U. Ostaszewska and K. Zajkowski},
     title = {Legendre-Fenchel {Transform} of the {Spectral} {Exponent} of {Analytic} {Functions} of {Weighted} {Composition} {Operators}},
     journal = {Journal of convex analysis},
     pages = {367--377},
     publisher = {mathdoc},
     volume = {18},
     number = {2},
     year = {2011},
     url = {http://geodesic.mathdoc.fr/item/JCA_2011_18_2_JCA_2011_18_2_a3/}
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U. Ostaszewska; K. Zajkowski. Legendre-Fenchel Transform of the Spectral Exponent of Analytic Functions of Weighted Composition Operators. Journal of convex analysis, Tome 18 (2011) no. 2, pp. 367-377. http://geodesic.mathdoc.fr/item/JCA_2011_18_2_JCA_2011_18_2_a3/