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Title: On the linear functionals associated to linearly related sequences of orthogonal polynomials
Authors: Petronilho, J. 
Keywords: Orthogonal polynomials; Moment linear functionals; Inverse problems; Locally convex spaces; Sobolev orthogonal polynomials
Issue Date: 2006
Citation: Journal of Mathematical Analysis and Applications. 315:2 (2006) 379-393
Abstract: 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.
Rights: openAccess
Appears in Collections:FCTUC Matemática - Artigos em Revistas Internacionais

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