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Cauchy transforms of characteristic functions and algebras generated by inner functions
Author(s):
Alec
L.
Matheson;
Michael
I.
Stessin
Journal:
Proc. Amer. Math. Soc.
133
(2005),
3361-3370.
MSC (2000):
Primary 46J10;
Secondary 46J15, 30D50, 30D55
Posted:
May 9, 2005
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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  .
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
DOI:
10.1090/S0002-9939-05-07913-X
PII:
S 0002-9939(05)07913-X
Received by editor(s):
May 5, 2004
Received by editor(s) in revised form:
June 28, 2004
Posted:
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 of article:
Copyright
2005,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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