Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4668882 | Bulletin des Sciences Mathématiques | 2015 | 14 Pages |
Abstract
We consider weighted sequence spaces on NN with increasing weights. Given a fixed integer k and a Hankel operator Γ on such a space, we show that the kth singular vector generates an analytic function with precisely k zeroes in the unit disc, in analogy with the classical AAK-theory of Hardy spaces. We also provide information on the structure of the singular spectrum for Hankel operators, applicable for instance to operators on the Dirichlet and Bergman spaces. Finally, we show by example that the connection between the classical AAK-theorem and rational approximation fails for the Dirichlet space.
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Physical Sciences and Engineering
Mathematics
Mathematics (General)
Authors
Fredrik Andersson, Marcus Carlsson, Karl-Mikael Perfekt,