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Article Dans Une Revue Pacific Journal of Mathematics Année : 2017

Compact composition operators with nonlinear symbols on the H2 space of Dirichlet series

Résumé

We investigate compactness of composition operators on the Hardy space of Dirichlet series induced by a map φ(s)=c0s+φ0(s), where φ0 is a Dirichlet polynomial. Our results depend heavily on the characteristic c0 of φ and, when c0=0, on both the degree of φ0 and its local behavior near a boundary point. We also study the approximation numbers for some of these operators. Our methods involve geometric estimates of Carleson measures and tools from differential geometry.
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hal-04605897 , version 1 (08-06-2024)

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Frédéric Bayart, Ole Brevig. Compact composition operators with nonlinear symbols on the H2 space of Dirichlet series. Pacific Journal of Mathematics, 2017, 291 (1), pp.81 - 120. ⟨10.2140/pjm.2017.291.81⟩. ⟨hal-04605897⟩
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