Quasi-definiteness of generalized Uvarov transforms of moment functionals

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

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

Journal of Applied Mathematics

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Volume 1 |Article ID 305256 | https://doi.org/10.1155/S1110757X01000225

D. H. Kim, K. H. Kwon, "Quasi-definiteness of generalized Uvarov transforms of moment functionals", Journal of Applied Mathematics, vol. 1, Article ID 305256, 22 pages, 2001. https://doi.org/10.1155/S1110757X01000225

Quasi-definiteness of generalized Uvarov transforms of moment functionals

D. H. Kim¹ and K. H. Kwon¹

¹Division of Applied Mathematics, Korea Advanced Institute of Science and Technology, Taejon 305-701, Korea

Received11 Mar 2001

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.

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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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