2005
DOI: 10.1007/s00009-005-0057-3
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Christoffel Transforms and Hermitian Linear Functionals

Abstract: Abstract. In this contribution we are focused on some spectral transformations of Hermitian linear functionals. They are the analogues of the Christoffel transform for linear functionals, i. e. for Jacobi matrices which has been deeply studied in the past. We consider Hermitian linear functionals associated with a probability measure supported on the unit circle. In such a case we compare the Hessenberg matrices associated with such a probability measure and its Christoffel transform. In this way, almost unita… Show more

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Cited by 19 publications
(22 citation statements)
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“…The perturbation dσ = |z − α| 2 dσ , |z| = 1, α ∈ C, is the so-called canonical Christoffel transformation (see [10]). …”
Section: Orthogonal Polynomials On the Unit Circle And Spectral Transmentioning
confidence: 99%
“…The perturbation dσ = |z − α| 2 dσ , |z| = 1, α ∈ C, is the so-called canonical Christoffel transformation (see [10]). …”
Section: Orthogonal Polynomials On the Unit Circle And Spectral Transmentioning
confidence: 99%
“…In [4] and [16] we have studied the connection between the associated Hessenberg matrices using the QR factorization. The iteration of the canonical Christoffel transformation has been analyzed in [8], [11], and [14].…”
Section: Introduction and Preliminary Resultsmentioning
confidence: 99%
“…We recover the Christoffel transformation when |Re(α)| 1. This transformation was studied in [4], [16]. Now, we study the relation between the Hessenberg matrix associated with L R , which will be denoted by H Y , and the Hessenberg matrix associated with L.…”
Section: )mentioning
confidence: 99%
See 1 more Smart Citation
“…The analogues on the unit circle to the canonical spectral transformations on the real line have been introduced by Marcellán and co-workers; see [3,5,6,9,10] and are known in the literature by Christoffel, Geronimus and Uvarov. Our goal in this section is to study the zeros of polynomials generated by these three perturbations for Szegő.…”
Section: Zeros and Canonical Spectral Transformationsmentioning
confidence: 99%