ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

8. Analysis

1991 MS Classification: 46E20 Stray, Arne Polynomial approximation of analytic functions with finite Dirichlet integral Let A denote the Hilbert space of all analytic functions in the unit disc D having finite Dirichlet integral. We characterize the relatively closed subsets F of D with the following property: If f is a function in A bounded on F, there are polynomials P_{n}, n = 1, 2 such that P_{n} converges to f in A and simultaneously pointwise boundedly to f on F.