Journal of Applied Mathematics
Volume 1 (2001), Issue 2, Pages 69-90

Quasi-definiteness of generalized Uvarov transforms of moment functionals

D. H. Kim and K. H. Kwon

Division of Applied Mathematics, Korea Advanced Institute of Science and Technology, Taejon 305-701, Korea

Received 11 March 2001

Copyright © 2001 D. H. Kim and K. H. Kwon. 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.


When σ is a quasi-definite moment functional with the monic orthogonal polynomial system {Pn(x)}n=0, we consider a point masses perturbation τ of σ given by τ:=σ+λΣl=1mΣk=0ml((1)kulk/k!)δ(k)(xcl), where λ,ulk, and cl are constants with cicj for ij. That is, τ is a generalized Uvarov transform of σ satisfying A(x)τ=A(x)σ, where A(x)=l=1m(xcl)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.