Skip to Main Content

Journal of the American Mathematical Society

Published by the American Mathematical Society, the Journal of the American Mathematical Society (JAMS) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6834 (online) ISSN 0894-0347 (print)

The 2020 MCQ for Journal of the American Mathematical Society is 4.79.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


Measures induced by analytic functions and a problem of Walter Rudin
HTML articles powered by AMS MathViewer

by Carl Sundberg PDF
J. Amer. Math. Soc. 16 (2003), 69-90 Request permission


The measure $\mu _\varphi$ induced by a bounded analytic function $\varphi$ on the unit disk $U$ may be defined by $\mu _\varphi (E)=m(\varphi ^{-1}(E))$, where $m$ is normalized Lebesgue measure on $\partial U$. 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 $\varphi$, not a constant multiple of an inner function, whose induced measure is rotationally symmetric. This function is not inner, but satisfies $\int \varphi \left (e^{i\theta }\right )^m\overline {\varphi \left (e^{i\theta }\right )^n} \frac {d\theta }{2\pi }=0$ if $m\ne n$, thus answering a question posed by Walter Rudin.
Similar Articles
  • Retrieve articles in Journal of the American Mathematical Society with MSC (2000): 30D50
  • Retrieve articles in all journals with MSC (2000): 30D50
Additional Information
  • Carl Sundberg
  • Affiliation: Department of Mathematics, University of Tennessee, Knoxville, Tennessee 37996-1300
  • Email:
  • 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
  • © Copyright 2002 American Mathematical Society
  • Journal: J. Amer. Math. Soc. 16 (2003), 69-90
  • MSC (2000): Primary 30D50
  • DOI:
  • MathSciNet review: 1937200