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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. | URI: | https://hdl.handle.net/10316/4617 | DOI: | 10.1016/j.jmaa.2005.05.018 | Rights: | openAccess |
Appears in Collections: | FCTUC Matemática - Artigos em Revistas Internacionais |
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