Subspaces of de Branges spaces with prescribed growth
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- by A. Baranov and H. Woracek
- St. Petersburg Math. J. 18 (2007), 699-716
- DOI: https://doi.org/10.1090/S1061-0022-07-00969-7
- Published electronically: August 9, 2007
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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.References
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Bibliographic 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
- Received by editor(s): April 22, 2006
- Published electronically: August 9, 2007
- © Copyright 2007 American Mathematical Society
- Journal: St. Petersburg Math. J. 18 (2007), 699-716
- MSC (2000): Primary 46E20; Secondary 46E22, 30D15
- DOI: https://doi.org/10.1090/S1061-0022-07-00969-7
- MathSciNet review: 2301039