Abstract
When σ
is a quasi-definite moment functional with the
monic orthogonal polynomial system {P n (x)}n=0∞, we consider a point masses perturbation τ
of σ
given by τ:=σ+λΣl=1 mΣk=0 ml((−1)kulk/k!)δ (k)(x − c l), where λ,ulk, and cl are
constants with ci≠cj
for i≠j. That is, τ
is a generalized Uvarov transform of
σ satisfying A(x) τ=A(x) σ, where
A(x)=∏l=1m(x−cl)ml+1. We find necessary and
sufficient conditions for τ
to be quasi-definite. We also
discuss various properties of monic orthogonal polynomial system
{Rn (x)}n=0∞
relative to τ
including
two examples.