Revisiting Biorthogonal Polynomials: An LU Factorization Discussion

The Gauss–Borel or LU factorization of Gram matrices bilinear forms is the pivotal element in discussion theory biorthogonal polynomials. construction families polynomials and its second kind functions, spectral modeling multiplication by independent variable x, Christoffel–Darboux kernel projection properties, are discussed from this point view. Then, Hankel case presented different specific case, as three terms relations, Heine formulas, Gauss quadrature formula given. classical orthogonal polynomial Hermite, Laguerre Jacobi type characterized within scheme. Finally, it shown who approach instrumental derivation Christoffel formulas for general Geronimus perturbations forms.