On second kind polynomials associated with rational transformations of linear functionals

In this paper the following construction process of orthogonal polynomials on the unit circle is considered: Let u   be a regular and hermitian linear functional and let {Φn}{Φn} be the corresponding orthogonal polynomials sequence. We define a new linear functional LL by means the following relation with u:λ(z−β)L=(z−α)u,α,β,λ∈C,λ≠0. In this situation we obtain conditions for the regularity of LL, as well as the corresponding orthogonal polynomials sequence. Also, we give one explicit representation for the orthogonal polynomials sequence of the second kind associated to LL. For the particular case when α=βα=β, LL becomes in the well-known modification of u by addition of a Dirac mass. This case will be studied with special attention.