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Poisson equation and discrete one-sided Hilbert transform for $(C,\alpha)$-bounded operators

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arxiv 2002.10122 v1 pith:SAPYNAPM submitted 2020-02-24 math.FA

Luciano Abadias , José E. Galé , Carlos Lizama This is my paper · ORCID
classification math.FA
keywords operatorsboundedequationhilbertone-sidedpoissontransformalpha
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We characterize the solutions of the Poisson equation and the domain of its associated one-sided Hilbert transform for Ces\`aro bounded operators of fractional order. The results obtained fairly generalize the corresponding ones for power-bounded operators. In passing, we give an extension of the mean ergodic theorem. Examples are given to illustrate the theory.

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  1. Operator inequalities I. Models and ergodicity

    math.FA 2019-08 accept novelty 7.0 of 10

    An operator with α(T*,T) ≥ 0 has an Agler-type functional model whenever k=1/α has summable Taylor coefficients satisfying a convolution decay condition, with no Nevanlinna-Pick sign restriction.

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