On the linear functionals associated to linearly related sequences of orthogona...

• Author(s): Petronilho, J.
• Date: 2006
• Persistent ID: http://hdl.handle.net/10316/4617
• Origin: Estudo Geral - Universidade de Coimbra
• Subject(s): Orthogonal polynomials; Moment linear functionals; Inverse problems; Locally convex spaces; Sobolev orthogonal polynomials
• Document Type: Article
• Language: English

Description

An inverse problem is solved, by stating that the regular linear functionals u and v associated to linearly related sequences of monic orthogonal polynomials (Pn)n and (Qn)n, respectively, in the sense for all n=0,1,2,... (where ri,n and si,n are complex numbers satisfying some natural conditions), are connected by a rational modification, i.e., there exist polynomials [phi] and [psi], with degrees M and N, respectively, such that [phi]u=[psi]v. We also make some remarks concerning the corresponding direct problem, stating a characterization theorem in the case N=1 and M=2. As an example, we give a linear relation of the above type involving Jacobi polynomials with distinct parameters. http://www.sciencedirect.com/science/article/B6WK2-4GDC0BW-4/1/c8bd62fc5b681b691284e86ce0b08d4e