Cauchy transforms of characteristic functions and algebras generated by inner functions
Authors:
Alec L. Matheson and Michael I. Stessin
Journal:
Proc. Amer. Math. Soc. 133 (2005), 33613370
MSC (2000):
Primary 46J10; Secondary 46J15, 30D50, 30D55
Published electronically:
May 9, 2005
MathSciNet review:
2161161
Fulltext PDF Free Access
Abstract 
References 
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Additional Information
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 closure of the polynomial algebra in these Cauchy transforms coincides with the 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 .
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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
DOI:
http://dx.doi.org/10.1090/S000299390507913X
PII:
S 00029939(05)07913X
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
Article copyright:
© Copyright 2005
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.
