On Negative Inertia of Pick Matrices Associated with Generalized Schur Functions View Full Text


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Article Info

DATE

2006-11

AUTHORS

Vladimir Bolotnikov, Alexander Kheifets

ABSTRACT

It is known [6] that for every function f in the generalized Schur class and every nonempty open subset Ω of the unit disk , there exist points z1,...,zn ∈Ω such that the n × nPick matrix has κ negative eigenvalues. In this paper we discuss existence of an integer n0 such that any Pick matrix based on z1,...,zn ∈Ω with n ≥ n0 has κ negative eigenvalues. Definitely, the answer depends on Ω. We prove that if , then such a number n0 does not exist unless f is a ratio of two finite Blaschke products; in the latter case the minimal value of n0 can be found. We show also that if the closure of Ω is contained in then such a number n0 exists for every function f in . More... »

PAGES

323-355

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/s00020-006-1428-2

DOI

http://dx.doi.org/10.1007/s00020-006-1428-2

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1028066478


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