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Transactions of the American Mathematical Society

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

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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An extremal problem for characteristic functions
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by Isabelle Chalendar, Stephan Ramon Garcia, William T. Ross and Dan Timotin PDF
Trans. Amer. Math. Soc. 368 (2016), 4115-4135 Request permission

Abstract:

Suppose $E$ is a subset of the unit circle $\mathbb {T}$ and $H^\infty \subset L^\infty$ is the Hardy subalgebra. We examine the problem of finding the distance from the characteristic function of $E$ to $z^nH^\infty$. This admits an alternate description as a dual extremal problem. Precise solutions are given in several important cases. The techniques used involve the theory of Toeplitz and Hankel operators as well as the construction of certain conformal mappings.
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Additional Information
  • Isabelle Chalendar
  • Affiliation: Institut Camille Jordan, University of Lyon I, 43 Boulevard du 11 Bovembre 1918, 69622 Villeurbanne cedex, France
  • MR Author ID: 612759
  • Email: chalendar@math.univ-lyon1.fr
  • Stephan Ramon Garcia
  • Affiliation: Department of Mathematics, Pomona College, Claremont, California 91711
  • MR Author ID: 726101
  • Email: Stephan.Garcia@pomona.edu
  • William T. Ross
  • Affiliation: Department of Mathematics and Computer Science, University of Richmond, Richmond, Virginia 23173
  • MR Author ID: 318145
  • Email: wross@richmond.edu
  • Dan Timotin
  • Affiliation: Simion Stoilow Institute of Mathematics of the Romanian Academy, P.O. Box 1-764, Bucharest 014700, Romania
  • Email: Dan.Timotin@imar.ro
  • Received by editor(s): July 10, 2013
  • Received by editor(s) in revised form: April 7, 2014
  • Published electronically: September 2, 2015
  • Additional Notes: The second author was partially supported by National Science Foundation Grant DMS-1001614
    The fourth author was partially supported by a grant of the Romanian National Authority for Scientific Research, CNCS Ð UEFISCDI, project number PN-II-ID-PCE-2011-3-0119.
  • © Copyright 2015 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 368 (2016), 4115-4135
  • MSC (2010): Primary 47A05, 47B35, 47B99
  • DOI: https://doi.org/10.1090/tran/6446
  • MathSciNet review: 3453366