6533b7d1fe1ef96bd125d6c4
RESEARCH PRODUCT
Mean ergodicity of weighted composition operators on spaces of holomorphic functions
David JornetEnrique JordáMaría J. Beltrán-meneuM. Carmen Gómez-colladosubject
Connected spaceComposition operatorApplied Mathematics010102 general mathematicsErgodicityMathematical analysisHolomorphic functionPower bounded operatorFixed pointHolomorphic function01 natural sciences010101 applied mathematicsMultiplication operatorMean ergodic operatorBounded functionWeighted composition operator0101 mathematicsMATEMATICA APLICADAComplex planeAnalysisMathematicsdescription
[EN] Let phi be a self-map of the unit disc D of the complex plane C and let psi be a holomorphic function on D. We investigate the mean ergodicity and power boundedness of the weighted composition operator C-phi,C-psi(f) = psi(f o phi) with symbol phi and multiplier psi on the space H(D). We obtain necessary and sufficient conditions on the symbol phi and on the multiplier psi which characterize when the weighted composition operator is power bounded and (uniformly) mean ergodic. One necessary condition is that the symbol phi has a fixed point in D. If phi is not a rational rotation, the sufficient conditions are related to the modulus of the multiplier on the fixed point of phi. Some of our results are valid in an open connected set U of the complex plane.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2016-12-01 |