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

Bolotnikov, V.; Kheifets, A.; Rodman, L.

doi:10.1090/S0002-9939-03-07096-5

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.

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