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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles 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 1.48.

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Notes on interpolation in the generalized Schur class. II. Nudel$’$man’s problem
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by D. Alpay, T. Constantinescu, A. Dijksma and J. Rovnyak PDF
Trans. Amer. Math. Soc. 355 (2003), 813-836 Request permission

Corrigendum: Trans. Amer. Math. Soc. 371 (2019), 3743-3745.

Abstract:

An indefinite generalization of Nudel$’$man’s problem is used in a systematic approach to interpolation theorems for generalized Schur and Nevanlinna functions with interior and boundary data. Besides known results on existence criteria for Pick-Nevanlinna and Carathéodory-Fejér interpolation, the method yields new results on generalized interpolation in the sense of Sarason and boundary interpolation, including properties of the finite Hilbert transform relative to weights. The main theorem appeals to the Ball and Helton almost-commutant lifting theorem to provide criteria for the existence of a solution to Nudel$’$man’s problem.
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Additional Information
  • D. Alpay
  • Affiliation: Department of Mathematics, Ben-Gurion University of the Negev, P.O. Box 653, 84105 Beer-Sheva, Israel
  • MR Author ID: 223612
  • Email: dany@math.bgu.ac.il
  • T. Constantinescu
  • Affiliation: Programs in Mathematical Sciences, University of Texas at Dallas, Box 830688, Richardson, Texas 75083-0688
  • Email: tiberiu@utdallas.edu
  • A. Dijksma
  • Affiliation: Department of Mathematics, University of Groningen, P.O. Box 800, 9700 AV Groningen, The Netherlands
  • MR Author ID: 58020
  • Email: dijksma@math.rug.nl
  • J. Rovnyak
  • Affiliation: University of Virginia, Department of Mathematics, P.O. Box 400137, Charlottesville, Virginia 22904-4137
  • MR Author ID: 151250
  • Email: rovnyak@Virginia.EDU
  • Received by editor(s): September 18, 2001
  • Received by editor(s) in revised form: April 16, 2002
  • Published electronically: October 9, 2002
  • Additional Notes: J. Rovnyak was supported by the National Science Foundation DMS-0100437 and by the Netherlands Organization for Scientific Research NWO B 61-482.
  • © Copyright 2002 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 355 (2003), 813-836
  • MSC (2000): Primary 47A57, 30E05, 47B32; Secondary 47B50, 42A50
  • DOI: https://doi.org/10.1090/S0002-9947-02-03148-3
  • MathSciNet review: 1932727