Open Access
5 August 2001 Quasi-definiteness of generalized Uvarov transforms of moment functionals
D. H. Kim, K. H. Kwon
J. Appl. Math. 1(2): 69-90 (5 August 2001). DOI: 10.1155/S1110757X01000225


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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D. H. Kim. K. H. Kwon. "Quasi-definiteness of generalized Uvarov transforms of moment functionals." J. Appl. Math. 1 (2) 69 - 90, 5 August 2001.


Published: 5 August 2001
First available in Project Euclid: 13 March 2003

zbMATH: 0996.33006
MathSciNet: MR1864295
Digital Object Identifier: 10.1155/S1110757X01000225

Primary: 33C45

Rights: Copyright © 2001 Hindawi

Vol.1 • No. 2 • 5 August 2001
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