Some examples of composition operators and their approximation numbers on the Hardy space of the bidisk
Copyright policy )Some examples of composition operators and their approximation numbers on the Hardy space of the bidisk
We give examples of composition operatorsCΦC_\PhionH2(D2)H^2 ({\mathbb D}^2)showing that the condition‖Φ‖∞=1\|\Phi \|_\infty = 1is not sufficient for their approximation numbersan(CΦ)a_n (C_\Phi )to satisfylimn→∞[an(CΦ)]1/n=1\lim _{n \to \infty } [a_n (C_\Phi ) ]^{1/\sqrt {n}} = 1, contrary to the11-dimensional case. We also give a situation where this implication holds. We make a link with the Monge–Ampère capacity of the image ofΦ\Phi.
- University of Seville Spain
- Artois University France
- University of Lille France
approximation numbers, Bergman spaces and Fock spaces, Hardy spaces, bidisk, Linear composition operators, Approximation by operators (in particular, by integral operators), Hardy space, Potentials and capacities, extremal length and related notions in higher dimensions, Functional Analysis (math.FA), \(H^p\)-spaces, Nevanlinna spaces of functions in several complex variables, Green capacity, Mathematics - Functional Analysis, weighted composition operator, Capacity theory and generalizations, composition operator, FOS: Mathematics, Bergman space, Monge-Ampère capacity, Spaces of operators; tensor products; approximation properties
approximation numbers, Bergman spaces and Fock spaces, Hardy spaces, bidisk, Linear composition operators, Approximation by operators (in particular, by integral operators), Hardy space, Potentials and capacities, extremal length and related notions in higher dimensions, Functional Analysis (math.FA), \(H^p\)-spaces, Nevanlinna spaces of functions in several complex variables, Green capacity, Mathematics - Functional Analysis, weighted composition operator, Capacity theory and generalizations, composition operator, FOS: Mathematics, Bergman space, Monge-Ampère capacity, Spaces of operators; tensor products; approximation properties
selected citations These citations are derived from selected sources.This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).3 popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.Average influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).Average impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.Average
Citations provided by BIP!Popularity provided by BIP!