Quasi-definiteness of generalized Uvarov transforms of moment functionals
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 tr...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2001-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/S1110757X01000225 |
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| Summary: | 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. |
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| ISSN: | 1110-757X 1687-0042 |