On a Symmetric Generalization of Bivariate Sturm-Liouville Problems

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Tefo Y. G., AKTAŞ R., Area I., Lekesiz E. G.

BULLETIN OF THE IRANIAN MATHEMATICAL SOCIETY, cilt.48, sa.4, ss.1649-1665, 2022 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 48 Sayı: 4
  • Basım Tarihi: 2022
  • Doi Numarası: 10.1007/s41980-021-00605-8
  • Dergi Adı: BULLETIN OF THE IRANIAN MATHEMATICAL SOCIETY
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH
  • Sayfa Sayıları: ss.1649-1665
  • Anahtar Kelimeler: Bivariate orthogonal polynomials, Symmetric orthogonal polynomials, Partial differential equations, MULTIVARIABLE ORTHOGONAL POLYNOMIALS, BASIC CLASS, DIFFERENCE-EQUATIONS, ASKEY TABLEAU, THEOREM
  • Ankara Üniversitesi Adresli: Evet

Özet

A new class of partial differential equations having symmetric orthogonal solutions is presented. The general equation is presented and orthogonality is obtained using the Sturm-Liouville approach. Conditions on the polynomial coefficients to have admissible partial differential equations are given. The general case is analyzed in detail, providing orthogonality weight function, three-term recurrence relations for the monic orthogonal polynomial solutions, as well as explicit form of these monic orthogonal polynomial solutions, which are solutions of an admissible and potentially self-adjoint linear second-order partial differential equation of hypergeometric type.