Journal of Applied Mathematics

Quasi-definiteness of generalized Uvarov transforms of moment functionals

D. H. Kim and K. H. Kwon

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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.

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J. Appl. Math., Volume 1, Number 2 (2001), 69-90.

First available in Project Euclid: 13 March 2003

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Primary: 33C45: Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) [See also 42C05 for general orthogonal polynomials and functions]


Kim, D. H.; Kwon, K. H. Quasi-definiteness of generalized Uvarov transforms of moment functionals. J. Appl. Math. 1 (2001), no. 2, 69--90. doi:10.1155/S1110757X01000225.

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