Spectral Transformations and Associated Linear Functionals of the First Kind

Given a quasi-definite linear functional u in the space of polynomials with complex coefficients, let us consider corresponding sequence monic orthogonal (SMOP short) (Pn)n≥0. For canonical Christoffel transformation u˜=(x−c)u SMOP (P˜n)n≥0, we are interested to study relation between u˜ and u(1)˜, where u(1) is for associated first kind (Pn(1))n≥0, u(1)˜=(x−c)u(1) its transformation. This problem also studied Geronimus transformations.