International Journal of Mathematics and Mathematical Sciences
Volume 6 (1983), Issue 3, Pages 459-466
Some remarks on the space
Department of Mathematics, University of Stockholm, Sweden
Received 26 April 1982; Revised 28 September 1982
Copyright © 1983 Claes Fernström. 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.
Let be a compact subset of the complex plane. We denote by the algebra consisting of the rational functions with poles off . The closure of in , , is denoted by . In this paper we consider the case . In section 2 we introduce the notion of weak bounded point evaluation of order and identify the existence of a weak bounded point evaluation of order , , as a necessary and sufficient condition for . We also construct a compact set such that has an isolated bounded point evaluation. In section 3 we examine the smoothness properties of functions in at those points which admit bounded point evaluations.