García Ardila, Juan CarlosMarcellán Español, Francisco José2022-06-082022-06-082021-06-01García-Ardila, J. C., & Marcellán, F. (2021). Spectral Transformations and Associated Linear Functionals of the First Kind. Axioms, 10(2), 107.2075-1680https://hdl.handle.net/10016/35030Given 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 a canonical Christoffel transformation ue = (x − c)u with SMOP (Pen)n≥0, we are interested to study the relation between ue and ug(1) , where u (1) is the linear functional for the associated orthogonal polynomials of the first kind (P (1) n )n≥0, and ug(1) = (x − c)u (1) is its Christoffel transformation. This problem is also studied for canonical Geronimus transformations.23eng© 2021 by the authors.Atribución 3.0 EspañaSpectral transformationDarboux transformationsFirst kind orthogonal polynomialsLaguerre-hahn linear functionalresearch articleMatemáticashttps://doi.org/10.3390/axioms10020107open access1223Axioms10AR/0000030759