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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Nevanlinna-Pick interpolation: Pick matrices have bounded number of negative eigenvalues


Authors: V. Bolotnikov, A. Kheifets and L. Rodman
Journal: Proc. Amer. Math. Soc. 132 (2004), 769-780
MSC (2000): Primary 41A05, 32A35
Published electronically: July 29, 2003
MathSciNet review: 2019954
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Abstract: The Nevanlinna-Pick interpolation problem is studied in the class of functions defined on the unit disk without a discrete set, with the property that all their Pick matrices have not more than a prescribed number of negative eigenvalues. It is shown, in particular, that the degenerate problem always has a unique solution, not necessarily meromorphic. A related extension problem to a maximal function in the class is also studied.


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Additional Information

V. Bolotnikov
Affiliation: Department of Mathematics, The College of William and Mary, Williamsburg, Virginia 23187-8795
Email: vladi@math.wm.edu

A. Kheifets
Affiliation: Department of Mathematics, The College of William and Mary, Williamsburg, Virginia 23187-8795
Email: sykhei@wm.edu

L. Rodman
Affiliation: Department of Mathematics, The College of William and Mary, Williamsburg, Virginia 23187-8795
Email: lxrodm@math.wm.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-03-07096-5
PII: S 0002-9939(03)07096-5
Keywords: Pick matrices, negative squares, Nevanlinna-Pick interpolation
Received by editor(s): September 12, 2002
Received by editor(s) in revised form: October 23, 2002
Published electronically: July 29, 2003
Additional Notes: The research of the third author was supported in part by NSF grant DMS-9988579
Communicated by: Joseph A. Ball
Article copyright: © Copyright 2003 American Mathematical Society