García Ardila, Juan CarlosMarcellán Español, Francisco José2022-07-152022-07-152021-06-28García-Ardila, J. C., & Marcellán, F. (2021). Spectral Transformations and Associated Linear Functionals of the First Kind. In Axioms (Vol. 10, Issue 2, p. 107). MDPI AG.2075-1680https://hdl.handle.net/10016/35471Given 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 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 (P(1)n)n≥0, and u(1)˜=(x−c)u(1) is its Christoffel transformation. This problem is also studied for canonical Geronimus transformations.23eng© 2021 by the authors. Licensee MDPI, Basel, Switzerland.Atribución 3.0 EspañaSpectral TransformationDarboux TransformationsFirst Kind Orthogonal PolynomialsLaguerre-Hahn Linear Functionalresearch articleMatemáticashttps://doi.org/10.3390/axioms10020107open access1223Axioms10AR/0000030759