|XXVIII Workshop on Geometric Methods in Physics||28.06-04.07.2009|
Legendre-Fenchel transform for the spectral exponent of polynomials of weighted composition operators
This is joint results with U. Ostaszewska.
We derive a relationship between the Legendre-Fenchel transform of the spectral exponent of weighted composition operators acting in $L^p$-spaces and the Legendre-Fenchel transform obtained for their polynomials. We establish the variational principle for the spectral exponent of polynomials of weighted composition operators.