95 citations · 892 across the 77 of their papers we have counts for
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Linear spectral transformations for multivariate orthogonal polynomials and multispectral Toda hierarchies
Gerardo Ariznabarreta, Manuel Mañas
Linear spectral transformations of orthogonal polynomials in the real line, and in particular Geronimus transformations, are extended to orthogonal polynomials depending on several…
Christoffel transformations for matrix orthogonal polynomials in the real line and the non-Abelian 2D Toda lattice hierarchy
Carlos Álvarez-Fernández, Gerardo Ariznabarreta, Juan Carlos García-Ardila +2
Given a matrix polynomial , matrix bi-orthogonal polynomials with respect to the sesquilinear form $\langle P(x),Q(x)\rangle_W=\int P(x) W(x)\operatorname{d}μ(x)(Q(x))^{\top}…
Multivariate orthogonal Laurent polynomials and integrable systems
Gerardo Ariznabarreta, Manuel Mañas
An ordering for Laurent polynomials in the algebraic torus , inspired by the Cantero-Moral-Velázquez approach to orthogonal Laurent polynomials in the unit circle,…
Darboux transformations for multivariate orthogonal polynomials
Gerardo Ariznabarreta, Manuel Mañas
Darboux transformations for polynomial perturbations of a real multivariate measure are found. The 1D Christoffel formula is extended to the multidimensional realm: multivariate or…