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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| _version_ | 1832564856034689024 |
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| author | D. H. Kim K. H. Kwon |
| author_facet | D. H. Kim K. H. Kwon |
| author_sort | D. H. Kim |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-dc524ffcb2df4db29c6f7ea16689e7ce |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2001-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-dc524ffcb2df4db29c6f7ea16689e7ce2025-02-03T01:10:04ZengWileyJournal of Applied Mathematics1110-757X1687-00422001-01-0112699010.1155/S1110757X01000225Quasi-definiteness of generalized Uvarov transforms of moment functionalsD. H. Kim0K. H. Kwon1Division of Applied Mathematics, Korea Advanced Institute of Science and Technology, Taejon 305-701, KoreaDivision of Applied Mathematics, Korea Advanced Institute of Science and Technology, Taejon 305-701, KoreaWhen 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.http://dx.doi.org/10.1155/S1110757X01000225 |
| spellingShingle | D. H. Kim K. H. Kwon Quasi-definiteness of generalized Uvarov transforms of moment functionals Journal of Applied Mathematics |
| title | Quasi-definiteness of generalized Uvarov transforms of moment functionals |
| title_full | Quasi-definiteness of generalized Uvarov transforms of moment functionals |
| title_fullStr | Quasi-definiteness of generalized Uvarov transforms of moment functionals |
| title_full_unstemmed | Quasi-definiteness of generalized Uvarov transforms of moment functionals |
| title_short | Quasi-definiteness of generalized Uvarov transforms of moment functionals |
| title_sort | quasi definiteness of generalized uvarov transforms of moment functionals |
| url | http://dx.doi.org/10.1155/S1110757X01000225 |
| work_keys_str_mv | AT dhkim quasidefinitenessofgeneralizeduvarovtransformsofmomentfunctionals AT khkwon quasidefinitenessofgeneralizeduvarovtransformsofmomentfunctionals |