2010
DOI: 10.1016/j.cam.2007.11.023
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Orthogonal polynomials and measures on the unit circle. The Geronimus transformations

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Cited by 22 publications
(27 citation statements)
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“…Later on, following the ideas of the spectral transformations associated with the spectral measures of Jacobi matrices (see [1], [18], [21]), in [3], [4], [13] some analog problems have been considered, mainly from the point of view of the Hessenberg matrices and their LU and QR factorization, respectively.…”
Section: Introduction and Preliminary Resultsmentioning
confidence: 99%
“…Later on, following the ideas of the spectral transformations associated with the spectral measures of Jacobi matrices (see [1], [18], [21]), in [3], [4], [13] some analog problems have been considered, mainly from the point of view of the Hessenberg matrices and their LU and QR factorization, respectively.…”
Section: Introduction and Preliminary Resultsmentioning
confidence: 99%
“…One of the reasons for studying this transformation is that it appears naturally when considering the Geronimus transformation (see [3,8]), defined by…”
Section: Introductionmentioning
confidence: 99%
“…The connection between the GGT matrix associated with a probability measure and the perturbed linear functional, respectively, in terms of their QR factorization instead of the LU factorization has been analyzed in [15,20,49]. More precisely, in [21], explicit expressions for polynomials orthogonal with respect to the perturbed measure have been obtained in terms of the orthogonal polynomials with respect to the initial probability measure.…”
Section: Ggt Matrixmentioning
confidence: 99%
“…A more general framework is presented in [28]. Besides, a special case of the Geronimus transformation has been analyzed in [20].…”
Section: Geronimus Transformationmentioning
confidence: 99%
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