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St. Petersburg Mathematical Journal
St. Petersburg Mathematical Journal
ISSN 1547-7371(online) ISSN 1061-0022(print)

 

Subspaces of de Branges spaces with prescribed growth


Authors: A. Baranov and H. Woracek
Original publication: Algebra i Analiz, tom 18 (2006), nomer 5.
Journal: St. Petersburg Math. J. 18 (2007), 699-716
MSC (2000): Primary 46E20; Secondary 46E22, 30D15
Published electronically: August 9, 2007
MathSciNet review: 2301039
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Abstract | References | Similar Articles | Additional Information

Abstract: The growth properties of de Branges spaces and their subspaces are studied. It is shown that, for each given pair of growth functions $ \lambda(r)=O(r)$ and $ \lambda_1=o(\lambda)$, there exist de Branges spaces of growth $ \lambda$ that have a de Branges subspace of growth $ \lambda_1$. This phenomenon cannot occur for a class of de Branges spaces that, in a certain sense, behave regularly along the real axis.


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Additional Information

A. Baranov
Affiliation: Department of Mathematics and Mechanics, St. Petersburg State University, Universitetskiĭ Prospect 28, Staryĭ Peterhof, St. Petersburg 198504, Russia
Email: antonbaranov@netscape.net

H. Woracek
Affiliation: Institute of Mathematics, Royal Institute of Technology (KTH), SE-100, 44, Stockholm, Sweden
Address at time of publication: Institut für Analysis und Scientific Computing, Technische Universität Wien, Wiedner Hauptstr. 8-10/101, A-1040, Wien, Austria
Email: harald.woracek@tuwien.ac.at

DOI: http://dx.doi.org/10.1090/S1061-0022-07-00969-7
PII: S 1061-0022(07)00969-7
Keywords: de Branges space, growth function, de Branges subspace
Received by editor(s): April 22, 2006
Published electronically: August 9, 2007
Article copyright: © Copyright 2007 American Mathematical Society