Article Dans Une Revue Journal of Mathematical Analysis and Applications Année : 2024

COMPOSITION OPERATORS ON DE BRANGES-ROVNYAK SPACES ASSOCIATED TO A RATIONAL (NOT INNER) FUNCTION

Résumé

In this paper, we characterize the boundedness, the compactness and the Hilbert-Schmidt property for composition operators acting from a de Branges-Rovnyak space $\mathcal H(b)$ into itself, when $b$ is a rational function in the closed unit ball of $H^\infty$ (but not a finite Blaschke product). In particular, we extend some of the results obtained by D. Sarason and J.N. Silva in the context of local Dirichlet spaces.

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hal-03844134 , version 1 (08-11-2022)

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Rim Alhajj, Emmanuel Fricain. COMPOSITION OPERATORS ON DE BRANGES-ROVNYAK SPACES ASSOCIATED TO A RATIONAL (NOT INNER) FUNCTION. Journal of Mathematical Analysis and Applications, 2024, 531 (1), 32 p. ⟨10.1016/j.jmaa.2023.127811⟩. ⟨hal-03844134⟩
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