Darboux transformations for orthogonal polynomials on the real line and on the unit circle

DOI10.1007/978-3-030-56190-1_3zbMath1460.33006OpenAlexW3129359125MaRDI QIDQ2658251

L. Velázquez, Leandro Moral, María José Cantero, Francisco Marcellán

Publication date: 19 March 2021

Full work available at URL: https://doi.org/10.1007/978-3-030-56190-1_3

zbMATH Keywords

orthogonal polynomialsDarboux transformationsJacobi and CMV matrices

Mathematics Subject Classification ID

Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis (42C05) Jacobi (tridiagonal) operators (matrices) and generalizations (47B36)

Cites Work

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• Darboux transformations for CMV matrices
• The Darboux process and time-and-band limiting for matrix orthogonal polynomials
• The classical moment problem as a self-adjoint finite difference operator
• Five-diagonal matrices and zeros of orthogonal polynomials on the unit circle
• The Darboux process and a noncommutative bispectral problem: some explorations and challenges
• Some Perspectives on the Eigenvalue Problem
• Factorization: little or great algorithm?

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