Composition Operators on the Dirichlet Space and Related Problems
Chacon, Gerardo A. · Chacon, Gerardo R. · Gimenez, Jose
Original · EN
In this paper we investigate the following problem: when a bounded analytic function ϕ on the unit disk D, fixing 0, is such that {ϕⁿ: n = 0, 1, 2,... } is orthogonal in D?, and consider the problem of characterizing the univalent, full self-maps of D in terms of the norm of the composition operator induced. The first problem is analogous to a celebrated question asked by W. Rudin on the Hardy space setting that was answered recently ([3] and [15]). The second problem is analogous to a problem investigated by J. Shapiro in [14] about characterization of inner functions in the setting of H².
English translation
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