Journal of Operator Theory

Volume 47, Issue 1, Winter 2002 pp. 63-77.

Overconvergence and cyclic vectors in Bergman spaces

Authors: John Akeroyd (1), and Kifah Alhami (2)
Author institution: (1) Department of Mathematics, University of Arkansa, Fayetteville, Arkansas 72701, USA
(2) Department of Mathematics, Jordan University of Science and Technology, P.O. Box 3030 Irbid, Jordan

Summary: In this paper we develop an overconvergence result in the context of polynomial approximation in the mean, primarily for certain weighted area measures. We then explore applications of this result pertaining to the existence and variety of cyclic vectors for the shift on Bergman spaces.

Keywords: Overconvergence, polynomial approximation, cyclic vectors, shift operator, Bergman spaces

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