Exceptional sets and Hilbert–Schmidt composition operators
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2003
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Elsevier
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Gallardo Gutiérrez, E. A. & González, M. J. «Exceptional Sets and Hilbert–Schmidt Composition Operators». Journal of Functional Analysis, vol. 199, n.o 2, abril de 2003, pp. 287-300. DOI.org (Crossref), https://doi.org/10.1016/S0022-1236(02)00006-X.
Abstract
It is shown that an analytic map phi of the unit disk into itself inducing a Hilbert-Schmidt composition operator on the Dirichlet space has the property that the set E-phi = {e(i0)is an element ofpartial derivativeD : \phi(e(10))\ = 1 has zero logarithmic capacity. We also show that this is no longer true for compact composition operators on the Dirichlet space. Moreover, such a condition is not even satisfied by Hilbert-Schmidt composition operators on the Hardy space.