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.
Copyright
Copyright © 2001 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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