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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Notes on interpolation in the generalized Schur class. II. Nudel$'$man's problem


Authors: D. Alpay, T. Constantinescu, A. Dijksma and J. Rovnyak
Journal: Trans. Amer. Math. Soc. 355 (2003), 813-836
MSC (2000): Primary 47A57, 30E05, 47B32; Secondary 47B50, 42A50
Published electronically: October 9, 2002
MathSciNet review: 1932727
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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
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
Email: dijksma@math.rug.nl

J. Rovnyak
Affiliation: University of Virginia, Department of Mathematics, P.O. Box 400137, Charlottesville, Virginia 22904-4137
Email: rovnyak@Virginia.EDU

DOI: http://dx.doi.org/10.1090/S0002-9947-02-03148-3
PII: S 0002-9947(02)03148-3
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.
Article copyright: © Copyright 2002 American Mathematical Society