Cauchy transforms of characteristic functions and algebras generated by inner functions
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- by Alec L. Matheson and Michael I. Stessin PDF
- Proc. Amer. Math. Soc. 133 (2005), 3361-3370 Request permission
Abstract:
We prove that Cauchy transforms of characteristic functions of subsets of positive measure of the unit circle are equidistributed in the unit disk in the sense that the $L^p$-closure of the polynomial algebra in these Cauchy transforms coincides with the $L^p$-closure of the polynomial algebra in a canonical inner function. As a corollary to this result we find conditions describing when the polynomial algebra in two singular inner functions determined by point masses is dense in the Hardy spaces $H^p$.References
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Additional Information
- Alec L. Matheson
- Affiliation: Department of Mathematics, Lamar University, Beaumont, Texas 77710
- Email: matheson@math.lamar.edu
- Michael I. Stessin
- Affiliation: Department of Mathematics and Statistics, University at Albany, SUNY, Albany, New York 12222
- Email: stessin@math.albany.edu
- Received by editor(s): May 5, 2004
- Received by editor(s) in revised form: June 28, 2004
- Published electronically: May 9, 2005
- Additional Notes: This work was accomplished while the first author was visiting the University at Albany. He thanks that institution for the hospitality extended during his visit.
- Communicated by: Joseph A. Ball
- © Copyright 2005
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 133 (2005), 3361-3370
- MSC (2000): Primary 46J10; Secondary 46J15, 30D50, 30D55
- DOI: https://doi.org/10.1090/S0002-9939-05-07913-X
- MathSciNet review: 2161161