Quasi‐definiteness of generalized Uvarov transforms of moment functionals

D. H. Kim and K. H. Kwon

Journal of Applied Mathematics, 2001, vol. 1, issue 2, 69-90

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.

Date: 2001
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https://doi.org/10.1155/S1110757X01000225

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnljam:v:1:y:2001:i:2:p:69-90

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