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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.

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A converse to a theorem of Adamyan, Arov and Krein
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by J. Agler and N. J. Young PDF
J. Amer. Math. Soc. 12 (1999), 305-333 Request permission

Abstract:

A well known theorem of Akhiezer, Adamyan, Arov and Krein gives a criterion (in terms of the signature of a certain Hermitian matrix) for interpolation by a meromorphic function in the unit disc with at most $m$ poles subject to an $L^\infty$-norm bound on the unit circle. One can view this theorem as an assertion about the Hardy space $H^2$ of analytic functions on the disc and its reproducing kernel. A similar assertion makes sense (though it is not usually true) for an arbitrary Hilbert space of functions. One can therefore ask for which spaces the assertion is true. We answer this question by showing that it holds precisely for a class of spaces closely related to $H^2$.
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Additional Information
  • J. Agler
  • Affiliation: Department of Mathematics, University of California at San Diego, La Jolla, California 92093
  • MR Author ID: 216240
  • Email: jagler@ucsd.edu
  • N. J. Young
  • Affiliation: Department of Mathematics, University of Newcastle, Newcastle upon Tyne NE1 7RU, England
  • Email: N.J.Young@ncl.ac.uk
  • Received by editor(s): May 28, 1997
  • Additional Notes: J. Agler’s research was supported by an NSF grant in Modern Analysis.
  • © Copyright 1999 American Mathematical Society
  • Journal: J. Amer. Math. Soc. 12 (1999), 305-333
  • MSC (1991): Primary 46E22; Secondary 47B38
  • DOI: https://doi.org/10.1090/S0894-0347-99-00291-X
  • MathSciNet review: 1643649