Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

# 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)

How to cite: García-Ardila, J.; Marcellán, F. Spectral Transformations and Associated Linear Functionals of the First Kind. Preprints 2021, 2021030626 (doi: 10.20944/preprints202103.0626.v1). García-Ardila, J.; Marcellán, F. Spectral Transformations and Associated Linear Functionals of the First Kind. Preprints 2021, 2021030626 (doi: 10.20944/preprints202103.0626.v1).

## 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.

## Subject Areas

Spectral transformation; Darboux transformations; First kind orthogonal polynomials; Laguerre-Hahn linear functional.

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