Three term relations for multivariate Uvarov orthogonal polynomials

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AKTAŞ R., Area I., Perez T. E.

COMPUTATIONAL & APPLIED MATHEMATICS, cilt.41, sa.7, 2022 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 41 Sayı: 7
  • Basım Tarihi: 2022
  • Doi Numarası: 10.1007/s40314-022-02030-x
  • Dergi Adı: COMPUTATIONAL & APPLIED MATHEMATICS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Applied Science & Technology Source, Computer & Applied Sciences, zbMATH
  • Anahtar Kelimeler: Multivariate orthogonal polynomials, Uvarov orthogonal polynomials, Moment linear functional, Modification of moment linear functionals, PARTIAL-DIFFERENTIAL-EQUATIONS, RECURSION FORMULAS
  • Ankara Üniversitesi Adresli: Evet

Özet

Three term relations for orthogonal polynomials in several variables associated to a moment linear functional obtained by a Uvarov modification of a given moment functional are studied. Existence of Uvarov orthogonal polynomials is analyzed, stating conditions to ensure it. The matrices of the three term relations of the Uvarov orthogonal polynomials are explicitly given in terms of the matrices of the three term relations satisfied by the original family. Two examples are presented in order to show that the results are valid for positive definite linear functionals and also for some quasi definite linear functionals which are not positive definite.