Quasi-definiteness of generalized Uvarov transforms of moment functionals

D. H. Kim and K. H. Kwon

Journal of Applied Mathematics, 2001, vol. 1, 1-22

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 + λ Σ l = 1   m Σ k = 0   m l ( ( − 1 ) k u l k / k ! ) δ   ( k ) ( x   −   c   l ) , where λ , u l k , and c l are constants with c i ≠c j for i ≠j . That is, τ is a generalized Uvarov transform of σ satisfying A ( x )   τ = A ( x )   σ , where A ( x ) = ∠l = 1 m ( x − c l ) m l + 1 . We find necessary and sufficient conditions for τ to be quasi-definite. We also discuss various properties of monic orthogonal polynomial system { R n   ( x ) } n = 0 ∞ relative to τ including two examples.

Date: 2001
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnljam:305256

DOI: 10.1155/S1110757X01000225

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