Multivariate orthogonal polynomials on non uniform lattices

• Autores: Yves Guemo Tefo
• Directores de la Tesis: Mama Foupouagnigni (dir. tes.), Iván Carlos Area Carracedo (dir. tes.)
• Lectura: En la Universidade de Vigo ( España ) en 2022
• Idioma: inglés
• Tribunal Calificador de la Tesis: Teresa Encarnacion Pérez Fernández (presid.), Ana Pilar Foulquié Moreno (secret.), Amilcar José Pinto Lopes Branqinho (voc.)
• Programa de doctorado: Programa de Doctorado en Agua, Sostenibilidad y Desarrollo por la Universidad de Vigo
• Materias:
  • Matemáticas
    • Análisis y análisis funcional
      • Teoría de la aproximación
      • Ecuaciones en diferencias
      • Funciones especiales
• Enlaces
  • Tesis en acceso abierto en: Investigo
• Resumen

  • In this PhD Thesis we investigate multivariate orthogonal polynomials on non uniform lattices. We have made a review of univariate classical orthogonal polynomials as well as their main properties. Then, we have introduced the notion of bivariate and multivariate orthogonal polynomials as well as a class of bivariate orthogonal polynomials satisfying some properties as those of the classical univariate orthogonal polynomials. In particular, We have analyzed properties related with moments, partial divided-difference equations as well as the bivariate symmetric case on a linear lattice. We have investigated some new properties and families of bivariate orthogonal polynomials and their application in the field of quasi- geostrophic shallow water.

    My contribution to the material in this thesis is contained in the following original papers: P1) I. Area, M. Foupouagnigni, E. Godoy, Y. Guemo Tefo. On moments of hypergeometric bivariate weight functions. Bulletin des Sciences Math ́ematiques 141 (2017) 766-784.

    P2) D. D. Tcheutia, Y. Guemo Tefo, M. Foupouagnigni, E. Godoy, I. Area. Linear Partial Divided- Difference Equation Satisfied by Multivariate Orthogonal Polynomials on Quadratic Lattices. Math. Model. Nat. Phenom., 12(3 (2017) 22–50.

    P3) D. D. Tcheutia, M. Foupouagnigni, Y. Guemo Tefo, I. Area. Divided-difference equation and three-term recurrence relations of some systems of bivariate q-orthogonal polynomials. Journal of Difference Equations and Applications 23(12) (2017) 2004–2036.

    P4) Y. Guemo Tefo, I. Area, M. Foupouagnigni. Bivariate Symmetric Discrete Orthogonal Polyno- mials. In “Advances in Real and Complex Analysis with Applications” (Michael Ruzhansky, Yeol Je Cho, Praveen Agarwal, Iv ́an Area, Editors) 87–106. ISSN: 978-981-10-4336-9.

    P5) I. Area, Y. Guemo Tefo. Monic bivariate polynomials on quadratic and q-quadratic lattices. Mediterranean Journal of Mathematics (accepted).

    P6) Y. Guemo Tefo, R. Akta ̧s, I. Area, E. Gu ̈ldo ̆gan-Lekesiz. On a symmetric generalization of bivariate Sturn-Liouville problems. Bulletin of the Iranian Mathematical Society (2021). https://doi.org/10.1007/s41980-021-00605-8.

    done in collaboration with my advisors (Professor Iv ́an Area and Professor Mama Foupouagnigni) and co-authored with Drs. R. Akta ̧s, E. Godoy, E. Gu ̈ldo ̆gan-Lekesiz, and D. D. Tcheutia.

    This thesis discusses some recent knowledge and investigation on orthogonal polynomials. The following are the main topics: (1) Divided-difference equations.

    (2) Moments.

    (3) Symmetric orthogonal polynomials.

    (4) Monic solutions.

    (5) Application to a problem related with water.