AAK-type theorems for Hankel operators on weighted spaces

Andersson, F., Carlsson, M. and Perfekt, K.-M. (2015) AAK-type theorems for Hankel operators on weighted spaces. Bulletin des Sciences Mathématiques, 139 (2). pp. 184-197. ISSN 0007-4497 doi: 10.1016/j.bulsci.2014.08.008

Abstract/Summary

We consider weighted sequence spaces on N 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.

Item Type	Article
URI	https://reading-clone.eprints-hosting.org/id/eprint/71515
Identification Number/DOI	10.1016/j.bulsci.2014.08.008
Refereed	Yes
Divisions	No Reading authors. Back catalogue items
Publisher	Elsevier
Download/View statistics	View download statistics for this item