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Approximation on Boundary Sets

Published online by Cambridge University Press:  20 November 2018

James Li-Ming Wang
James Li-Ming Wang*
Affiliation:
Department of Mathematics, University of Alabama, University, Alabama 35486
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Abstract

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Let U be a bounded open subset of the complex plane. By a well known result of A. M. Davie, C(bU) is the uniformly-closed linear span of A(U) and the powers (z-zi)-n, n = 1, 2, 3, … with zi a point in each component of U. We show that if A(U) is a Dirichlet algebra and bU is of infinite length, then one power of (z - zi) is superfluous.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 22 , Issue 3 , 01 September 1979 , pp. 377 - 379
Copyright
Copyright © Canadian Mathematical Society 1979

References

1. Davie, A. M., Dirichlet Algebras of Analytic Functions, J. Functional Analysis, 6 (1970), 348-356.Google Scholar
2. Davie, A. M., Bounded Approximation and Dirichlet Sets, J. Functional Analysis, 6 (1970), 460-467.Google Scholar
3. Duren, P., Theory of Hp Spaces, Academic Press, New York, 1970.Google Scholar
4. Gamelin, T. W., Uniform Algebras, Prentice-Hall, Englewood Cliffs, New Jersey, 1969.Google Scholar
5. Gamelin, T. W. and Garnett, J., Pointwise Bounded Approximation and Dirichlet Algebras, J. Functional Analysis, 8 (1971), 360-404.Google Scholar
6. Korevaar, J., and Pfluger, P., Spanning sets of powers on wild Jordan curves, Nederl. Akad. Wetensch. Proc. Ser. A, 77 (1974), 293-305.Google Scholar
7. O'Farrell, A. G., A generalized Walsh-Lebesgue theorem, Proc. Roy. Soc. Edinburgh, to appear.Google Scholar
8. Pietz, K., Cauchy Transforms and Characteristic Functions, Pac. J. Math., 58 (1975), 563-568.Google Scholar
9. Wermer, J., Nonrectifiable simple closed curve, Advanced Problems and solutions, Amer. Math. Monthly 64 (1957), 372.Google Scholar