Point evaluations and polynomial approximation in the mean with respect to harmonic measure

Author:
John Akeroyd

Journal:
Proc. Amer. Math. Soc. **105** (1989), 575-581

MSC:
Primary 46E15; Secondary 30E10, 30H05

MathSciNet review:
929403

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: For and crescents , with harmonic measure , the author examines the collection of bounded point evaluations, , (resp. analytic bounded point evaluations, ) for polynomials with respect to the norm. If the polynomials are dense in the generalized Hardy space , then (Theorem 4). If the polynomials are not dense in , then (with a mild restriction on ) (Theorem 7).

**[1]**John Akeroyd,*Polynomial approximation in the mean with respect to harmonic measure on crescents*, Trans. Amer. Math. Soc.**303**(1987), no. 1, 193–199. MR**896016**, 10.1090/S0002-9947-1987-0896016-X**[2]**James E. Brennan,*Point evaluations, invariant subspaces and approximation in the mean by polynomials*, J. Funct. Anal.**34**(1979), no. 3, 407–420. MR**556263**, 10.1016/0022-1236(79)90084-3**[3]**Peter L. Duren,*Theory of 𝐻^{𝑝} spaces*, Pure and Applied Mathematics, Vol. 38, Academic Press, New York-London, 1970. MR**0268655****[4]**T. W. Gamelin,*Uniform algebras*, Chelsea, New York, 1984.

Retrieve articles in *Proceedings of the American Mathematical Society*
with MSC:
46E15,
30E10,
30H05

Retrieve articles in all journals with MSC: 46E15, 30E10, 30H05

Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1989-0929403-9

Article copyright:
© Copyright 1989
American Mathematical Society