Some remarks on the space R 2 ( E )

Claes Fernström

International Journal of Mathematics and Mathematical Sciences, 1983, vol. 6, 1-8

Abstract:

Let E be a compact subset of the complex plane. We denote by R ( E ) the algebra consisting of the rational functions with poles off E . The closure of R ( E ) in L p ( E ) , 1 ≤ p < ∞ , is denoted by R p ( E ) . In this paper we consider the case p = 2 . In section 2 we introduce the notion of weak bounded point evaluation of order β and identify the existence of a weak bounded point evaluation of order β , β > 1 , as a necessary and sufficient condition for R 2 ( E ) ≠ L 2 ( E ) . We also construct a compact set E such that R 2 ( E ) has an isolated bounded point evaluation. In section 3 we examine the smoothness properties of functions in R 2 ( E ) at those points which admit bounded point evaluations.

Date: 1983
References: Add references at CitEc
Citations:

Downloads: (external link)
http://downloads.hindawi.com/journals/IJMMS/6/826854.pdf (application/pdf)
http://downloads.hindawi.com/journals/IJMMS/6/826854.xml (text/xml)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:826854

DOI: 10.1155/S016117128300040X

Access Statistics for this article

More articles in International Journal of Mathematics and Mathematical Sciences from Hindawi
Bibliographic data for series maintained by Mohamed Abdelhakeem ().