Remote Access St. Petersburg Mathematical Journal

St. Petersburg Mathematical Journal

ISSN 1547-7371(online) ISSN 1061-0022(print)



Majorization in de Branges spaces. III. Division by Blaschke products

Authors: A. Baranov and H. Woracek
Original publication: Algebra i Analiz, tom 21 (2009), nomer 6.
Journal: St. Petersburg Math. J. 21 (2010), 843-875
MSC (2010): Primary 46E15, 46E22, 30J10
Published electronically: September 22, 2010
MathSciNet review: 2604541
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in St. Petersburg Mathematical Journal with MSC (2010): 46E15, 46E22, 30J10

Retrieve articles in all journals with MSC (2010): 46E15, 46E22, 30J10

Additional Information

A. Baranov
Affiliation: Department of Mathematics and Mechanics, St. Petersburg State University, Universitetskiĭ Prospekt 28, Staryĭ Peterhof, St. Petersburg 198504, Russia

H. Woracek
Affiliation: Institut für Analysis und Scientific Computing, Technische Universität Wien, Wiedner Hauptstrasse 8–10/101, A–1040 Wien, Austria

Keywords: de Branges subspace, majorant, subharmonic function, Blaschke product
Received by editor(s): September 22, 2009
Published electronically: September 22, 2010
Dedicated: Dedicated to Victor Petrovich Havin on the occasion of his 75th birthday
Article copyright: © Copyright 2010 American Mathematical Society

American Mathematical Society