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AAK-type theorems for Hankel operators on weighted spaces
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- Andersson, Fredrik (author)
- Lund University,Lunds universitet,Matematik LTH,Matematikcentrum,Institutioner vid LTH,Lunds Tekniska Högskola,Mathematics (Faculty of Engineering),Centre for Mathematical Sciences,Departments at LTH,Faculty of Engineering, LTH
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- Carlsson, Marcus (author)
- Lund University,Lunds universitet,Matematikcentrum,Institutioner vid LTH,Lunds Tekniska Högskola,Centre for Mathematical Sciences,Departments at LTH,Faculty of Engineering, LTH
- Perfekt, Karl-Mikael (author)
- (creator_code:org_t)
- Elsevier BV, 2015
- 2015
- English.
- In: Bulletin des Sciences Mathématiques. - : Elsevier BV. - 0007-4497. ; 139:2, s. 184-197
- Journal article (peer-reviewed)
Abstract
Subject headings
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- We consider weighted sequence spaces on N with increasing weights. Given a fixed integer k and a Hankel operator Gamma 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. (c) 2014 Elsevier Masson SAS. All rights reserved.
Subject headings
- NATURVETENSKAP -- Data- och informationsvetenskap -- Datorseende och robotik (hsv//swe)
- NATURAL SCIENCES -- Computer and Information Sciences -- Computer Vision and Robotics (hsv//eng)
- NATURVETENSKAP -- Matematik (hsv//swe)
- NATURAL SCIENCES -- Mathematics (hsv//eng)
Keyword
- Singular vectors
- Schmidt pairs
- Henkel operators
- AAK theory
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- art (subject category)
- ref (subject category)
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