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Spectral Transformations and Associated Linear Functionals of the First Kind
Version 1
: Received: 24 March 2021 / Approved: 25 March 2021 / Online: 25 March 2021 (14:40:48 CET)
A peer-reviewed article of this Preprint also exists.
García-Ardila, J.C.; Marcellán, F. Spectral Transformations and Associated Linear Functionals of the First Kind. Axioms 2021, 10, 107. García-Ardila, J.C.; Marcellán, F. Spectral Transformations and Associated Linear Functionals of the First Kind. Axioms 2021, 10, 107.
Abstract
Given a quasi-definite linear functional u in the linear space of polynomials with complex coefficients let us consider the corresponding sequence of monic orthogonal polynomials (SMOP in short) (Pn)n≥0. For the Christoffel transformation u˜=(x−c)u with SMOP (P˜n)n≥0, we are interested to study the relation between u˜ and u(1)˜, where u(1) is the linear functional for the associated orthogonal polynomials of the first kind (Pn(1))n≥0 and u(1)˜=(x−c)u(1) is its Christoffel transformation. This problem is also studied for the Geronimus transformations.
Keywords
Spectral transformation; Darboux transformations; First kind orthogonal polynomials; Laguerre-Hahn linear functional.
Subject
Computer Science and Mathematics, Algebra and Number Theory
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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