Some remarks on optimal interpolation
type: Item
instance of: scholarly article
title: Some remarks on optimal interpolation
zbMATH Open document ID: 0661.93026
DOI: 10.1016/0167-6911(88)90068-0
author: Allen Tannenbaum
author: Ciprian Foias
published in: Systems \& Control Letters
publication date: 1988-01-01T00:00:00Z
review text: Let \(\theta\) be a non-constant (scalar) inner function, and let T be the compression of the canonical shift on \(H^ 2\) to the subspace \(H^ 2\ominus \theta H^ 2\) (all \(H^ p\) spaces are with respect to the unit disc). For a rational function \(w\in H^{\infty}\), consider the operator w(T). An efficient procedure is described for calculation of singular values for w(T). The approach is based on the skew Toeplitz operator \(A_{\rho}\) (depending on the positive parameter \(\rho)\) defined by \(A_{\rho}=q(T)q(T)^*-\rho^{-2}p(T)p(T)^*,\) where \(w=p/q\) and p and q are polynomials.
Mathematics Subject Classification ID: 93B35
Mathematics Subject Classification ID: 30D55
Mathematics Subject Classification ID: 47B35
Mathematics Subject Classification ID: 93B28
Mathematics Subject Classification ID: 30E05
Mathematics Subject Classification ID: 46E15
zbMATH DE Number: 4081395
zbMATH Keywords: compression of the canonical shift
zbMATH Keywords: singular values
zbMATH Keywords: skew Toeplitz operator
reviewed by: Leiba Rodman
MaRDI profile type: Publication
full work available at URL: 0167-6911(88)90068-0
OpenAlex ID: W2012772898
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description: scientific article; zbMATH DE number 4081395