Nevanlinna–Pick interpolation: Pick matrices have bounded number of negative eigenvalues
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- by V. Bolotnikov, A. Kheifets and L. Rodman PDF
- Proc. Amer. Math. Soc. 132 (2004), 769-780 Request permission
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.References
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Additional Information
- V. Bolotnikov
- Affiliation: Department of Mathematics, The College of William and Mary, Williamsburg, Virginia 23187-8795
- MR Author ID: 266846
- 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
- 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
- © Copyright 2003 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 132 (2004), 769-780
- MSC (2000): Primary 41A05, 32A35
- DOI: https://doi.org/10.1090/S0002-9939-03-07096-5
- MathSciNet review: 2019954