Quasi-definiteness of generalized Uvarov transforms of moment functionals

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When σ is a quasi-definite moment functional with themonic orthogonal polynomial system {Pn (x)}n=0=0, we consider a point masses perturbation τ of σ given by τ: = σ + λ Σ l=1 Σk=0 ((- 1)ulk/k!) δ (x-cl), where λ, ulk, and cl areconstants 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 = 1 (x - cl)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.
Publisher
Hindawi Publishing Corporation
Issue Date
2001
Language
English
Citation

JOURNAL OF APPLIED MATHEMATICS, v.1, no.2, pp.69 - 90

ISSN
1110-757X
URI
http://hdl.handle.net/10203/83778
Appears in Collection
MA-Journal Papers(저널논문)
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