Measures induced by analytic functions and a problem of Walter Rudin
Author:
Carl Sundberg
Journal:
J. Amer. Math. Soc. 16 (2003), 6990
MSC (2000):
Primary 30D50
Published electronically:
September 10, 2002
MathSciNet review:
1937200
Fulltext PDF Free Access
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Abstract: The measure induced by a bounded analytic function on the unit disk may be defined by , where is normalized Lebesgue measure on . We discuss the problem of characterizing such measures, and produce some necessary conditions which we conjecture are sufficient. Our main results are a construction showing that our conjectured sufficient conditions are sufficient for a measure to be weakly approximable by induced measures, and a construction of a function , not a constant multiple of an inner function, whose induced measure is rotationally symmetric. This function is not inner, but satisfies if , thus answering a question posed by Walter Rudin.
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Additional Information
Carl Sundberg
Affiliation:
Department of Mathematics, University of Tennessee, Knoxville, Tennessee 379961300
Email:
sundberg@math.utk.edu
DOI:
http://dx.doi.org/10.1090/S0894034702004046
PII:
S 08940347(02)004046
Received by editor(s):
May 5, 2000
Received by editor(s) in revised form:
August 5, 2002
Published electronically:
September 10, 2002
Additional Notes:
Research supported in part by the National Science Foundation
Article copyright:
© Copyright 2002
American Mathematical Society
