A note on the Geronimus transformation and Sobolev orthogonal polynomials

DOI10.1007/s11075-013-9788-6zbMath1306.42043arXiv1308.4364OpenAlexW2050333631MaRDI QIDQ466853

Maxim Derevyagin, Francisco Marcellán

Publication date: 31 October 2014

Published in: Numerical Algorithms (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1308.4364

zbMATH Keywords

orthogonal polynomialsJacobi matricesCholesky decompositionGeronimus transformationSobolev inner products

Mathematics Subject Classification ID

Factorization of matrices (15A23) Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis (42C05)

Related Items (17)

Recurrence relations for the moments of discrete semiclassical orthogonal polynomials ⋮ Darboux transformations for CMV matrices ⋮ An extension of the Geronimus transformation for orthogonal matrix polynomials on the real line ⋮ Discrete semiclassical orthogonal polynomials of class 2 ⋮ DEK-type orthogonal polynomials and a modification of the Christoffel formula ⋮ Higher-order recurrence relations, Sobolev-type inner products and matrix factorizations ⋮ Complex Jacobi matrices generated by Darboux transformations ⋮ Multiple Geronimus transformations ⋮ On Sobolev orthogonal polynomials ⋮ Asymptotics of orthogonal polynomials generated by a Geronimus perturbation of the Laguerre measure ⋮ A canonical Geronimus transformation for matrix orthogonal polynomials ⋮ Orthogonality of the Dickson polynomials of the $(k+1)$-th kind ⋮ Christoffel transformation for a matrix of bi-variate measures ⋮ Geronimus transformations of bivariate linear functionals ⋮ Geronimus transformations for sequences of \(d\)-orthogonal polynomials ⋮ Associated orthogonal polynomials of the first kind and Darboux transformations ⋮ Matrix biorthogonal polynomials on the real line: Geronimus transformations

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