Revisiting biorthogonal polynomials: an \(LU\) factorization discussion

DOI10.1007/978-3-030-56190-1_10zbMath1460.33011arXiv1907.04280OpenAlexW2959770022MaRDI QIDQ2658259

Manuel Mañas

Publication date: 19 March 2021

Full work available at URL: https://arxiv.org/abs/1907.04280

zbMATH Keywords

Gram matrixbiorthogonal polynomialsJacobi matrixsesquilinear formsGauss-Borel factorizationChristoffel formulasbivariate functionalsChristoffel perturbationsGeronimus perturbationsquasi determinantsvery classical orthogonal polynomials

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)

Related Items (1)

Positive bidiagonal factorization of tetradiagonal Hessenberg matrices

Cites Work

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• Multivariate orthogonal polynomials and integrable systems
• Orthogonal Laurent polynomials on the unit circle, extended CMV ordering and 2D Toda type integrable hierarchies
• Matrix orthogonal Laurent polynomials on the unit circle and Toda type integrable systems
• On the Christoffel-Darboux formula for generalized matrix orthogonal polynomials
• Multiple orthogonal polynomials of mixed type: Gauss-Borel factorization and the multi-component 2D Toda hierarchy
• Moment matrices and multi-component KP, with applications to random matrix theory
• Polynomial perturbations of bilinear functionals and Hessenberg matrices
• Transformation groups for soliton equations. Euclidean Lie algebras and reduction of the KP hierarchy
• Complete integrability of the Kadomtsev-Petviashvili equation
• Rational spectral transformations and orthogonal polynomials
• Generalized orthogonal polynomials, discrete KP and Riemann-Hilbert problems.
• Christoffel transformations for multivariate orthogonal polynomials
• The Schur complement and its applications
• Quasideterminants
• Darboux transformation and perturbation of linear functionals
• Partitions, vertex operator constructions and multi-component KP equations
• A Jacobi type Christoffel-Darboux formula for multiple orthogonal polynomials of mixed type
• On Multivariate Interpolation
• The multicomponent 2D Toda hierarchy: generalized matrix orthogonal polynomials, multiple orthogonal polynomials and Riemann–Hilbert problems
• The multicomponent 2D Toda hierarchy: discrete flows and string equations
• The multicomponent 2D Toda hierarchy: dispersionless limit
• Non-Abelian integrable hierarchies: matrix biorthogonal polynomials and perturbations
• CMV Biorthogonal Laurent Polynomials: Perturbations and Christoffel Formulas
• The n-component KP hierarchy and representation theory
• Matrix biorthogonal polynomials on the real line: Geronimus transformations
• The connection between systems of polynomials orthogonal with respect to different distribution functions
• Integrable Systems from the Classical Reflection Equation

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