The inverse problem for linearly related orthogonal polynomials: General case

2018/10/03 by Ana Peña, Peña, A., M.L. Rezola +1
Computer Science · Mathematics · #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Iterative Methods for Nonlinear Equations #Mathematical functions and polynomials #Matrix Theory and Algorithms

paper · pdf · doi:10.48550/arxiv.1810.01691

openalex publication_date 2018/10/03 · openalex created_date 2018/10/12 · openalex updated_date 2026/07/28

Abstract

We study the inverse problem in the theory of (standard) orthogonal polynomials involving two polynomials families (P_n)_n and (Q_n)_n which are connected by a linear algebraic structure such as P_n(x)+∑_i=1^N r_i,nP_n-i(x)=Q_n(x)+∑_i=1^M s_i,nQ_n-i(x) for all n=0,1, … where N and M are arbitrary nonnegative integer numbers.

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• A family of orthogonal polynomials corresponding to Jacobi matrices with a trace class inverse
• Orthogonal polynomials associated with an inverse quadratic spectral transform
• A structure relation for some specific orthogonal polynomials
• Explicit Inversions of Certain Matrices II