Hostname: page-component-cd9895bd7-8ctnn Total loading time: 0 Render date: 2024-12-26T01:44:18.148Z Has data issue: false hasContentIssue false
  • English
  • Français

14.—A Generalised Walsh-Lebesgue Theorem*

Published online by Cambridge University Press:  14 February 2012

A. G. O'Farrell
A. G. O'Farrell
Affiliation:
University of California, Los Angeles
Get access Rights & Permissions [Opens in a new window]

Synopsis

Let X be the boundary of a compact set which does not separate the plane, C. Let Φ and Ψ be homeomorphisms of C to C with opposite orientations. Then every continuous complex-valued function on X is the uniform limit on X of sums p(Φ)+q(ψ), where p and q are analytic polynomials.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 73 , 1975 , pp. 231 - 234
Copyright
Copyright © Royal Society of Edinburgh 1975

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1Browder, A. and Wermer, J., A method for constructing Dirichlet algebras. Proc. Amer. Math. Soc, 15, 546–552, 1964.CrossRefGoogle Scholar
2Ohtsuka, M., Dirichlet problem, extremal length and prime ends. Van Nostrand Math. Studies, 20, 1970.Google Scholar
3Preskenis, K., Approximation on discs. Trans. Amer. Math. Soc, 171, 445–467, 1972.CrossRefGoogle Scholar
4Wermer, J., Seminar über Funktionen-Algebren. Lecture Notes Math., 1, 1964.Google Scholar