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Functional analysis
- Publisher
- Wiley
- Copyright
- © London Mathematical Society
- ISSN
- 0024-6093
- eISSN
- 1469-2120
- DOI
- 10.1112/blms/bdu067
- Publisher site
- See Article on Publisher Site
Abstract
Let X be a compact nowhere dense subset of the complex plane C, and let R(X) be the uniform closure of the rational functions having no poles on X. We present a short proof of the fact that each non‐peak point for R(X) admits a representing measure absolutely continuous with respect area. If X happens to have finite perimeter, then every non‐peak point admits a representing measure absolutely continuous with respect to arc length, provided the corresponding integral is taken in a principal value sense.
Journal
Bulletin of the London Mathematical Society – Wiley
Published: Dec 1, 2014