Spectral theory for bounded banded matrices with positive bidiagonal factorization and mixed multiple orthogonal polynomials
Amílcar Branquinho, Ana Foulquié‐Moreno, Manuel Mañas
Abstract
Spectral and factorization properties of oscillatory matrices lead to a spectral Favard theorem for bounded banded matrices, that admit a positive bidiagonal factorization, in terms of sequences of mixed multiple orthogonal polynomials with respect to a set positive Lebesgue–Stieltjes measures. A mixed multiple Gauss quadrature formula with corresponding degrees of precision is given.
Topics & Concepts
MathematicsFactorizationOrthogonal polynomialsBounded functionPure mathematicsRiemann–Stieltjes integralSpectral theoremMathematical analysisAlgorithmIntegral equationOperator theoryMatrix Theory and AlgorithmsMathematical functions and polynomialsSpectral Theory in Mathematical Physics