International Journal of Mathematics and Mathematical Sciences
Volume 22 (1999), Issue 4, Pages 739-744
doi:10.1155/S0161171299227391

On cyclicity in weighted Dirichlet spaces

F. Jafari1 and R. Raposa2

1Department of Mathematics, University of Wyoming, Laramie 82071-3036, WY, USA
2Department of Math and CS, Montana State University, Billings 59101, MT, USA

Received 6 August 1997; Revised 17 February 1998

Copyright © 1999 F. Jafari and R. Raposa. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We extend some results of Brown and Shields on cyclicity to weighted Dirichlet spaces 0<α<1. We prove a comparison theorem for cyclicity in these spaces and provide a result on the geometry of the family of cyclic vectors in general functional Hilbert spaces.