Quasi-definiteness of generalized Uvarov transforms of moment functionals

Kim, D. H.; Kwon, K. H.

doi:https://doi.org/10.1155/S1110757X01000225

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.

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.

Journal of Applied Mathematics

Quasi-definiteness of generalized Uvarov transforms of moment functionals

Abstract

Copyright

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