Majorization in de Branges spaces. III. Division by Blaschke products
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- by A. Baranov and H. Woracek
- St. Petersburg Math. J. 21 (2010), 843-875
- DOI: https://doi.org/10.1090/S1061-0022-2010-01122-1
- Published electronically: September 22, 2010
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Abstract:
This paper is a part of a series dealing with subspaces of de Branges spaces of entire functions generated by majorization on subsets of the closed upper half-plane. In the present, third, part the study of a certain Banach space generated by an admissible majorant is continued. The main theme is “invariance of the unit ball with respect to division by Blaschke products”. In connection with this topic, representability via special types of majorants plays an important role. Some (positive and negative) results on invariance under division by Blaschke factors are obtained, and the unit balls representable by $\log$-superharmonic majorants are characterized.References
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Bibliographic Information
- A. Baranov
- Affiliation: Department of Mathematics and Mechanics, St. Petersburg State University, Universitetskiĭ Prospekt 28, Staryĭ Peterhof, St. Petersburg 198504, Russia
- Email: a.baranov@ev13934.spb.edu
- H. Woracek
- Affiliation: Institut für Analysis und Scientific Computing, Technische Universität Wien, Wiedner Hauptstrasse 8–10/101, A–1040 Wien, Austria
- Email: harald.woracek@tuwien.ac.at
- Received by editor(s): September 22, 2009
- Published electronically: September 22, 2010
- © Copyright 2010 American Mathematical Society
- Journal: St. Petersburg Math. J. 21 (2010), 843-875
- MSC (2010): Primary 46E15, 46E22, 30J10
- DOI: https://doi.org/10.1090/S1061-0022-2010-01122-1
- MathSciNet review: 2604541
Dedicated: Dedicated to Victor Petrovich Havin on the occasion of his 75th birthday