Applications of functions satisfying certain recurrence relations

• Grant number: 17/04358-8
• Support Opportunities: Scholarships in Brazil - Doctorate (Direct)
• Start date: April 01, 2017
• End date: February 28, 2019
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Applied Mathematics
• Principal Investigator: Alagacone Sri Ranga
• Grantee: Luana de Lima Silva Ribeiro
• Host Institution: Instituto de Biociências, Letras e Ciências Exatas (IBILCE). Universidade Estadual Paulista (UNESP). Campus de São José do Rio Preto. São José do Rio Preto , SP, Brazil
• Associated research grant: 16/09906-0 - Harmonic analysis, approximation theory and applications, AP.TEM

Abstract

Recently, in a publication of the supervisor of this project, it was established that a sequence of orthogonal polynomials on the unit circle can be characterized by a pair of real sequences $\{c_n\}_{n \geq 1}$ and $\{d_{n}\}_{n \geq 1}$, where the second sequence is also a positive chain sequence. This opened up a new line of investigation of the properties and applications of the associated polynomials. Thus, one of the principal objective of our research for the next few years is to study the properties of orthogonal polynomials on the unit circle starting from the sequences $\{c_n\}_{n \geq 1}$ and $\{d_{n}\}_{n \geq 1}$, and also the applications of functions $\{\mathcal{W}_{n}(x)\}_{n \geq 0}$ and the polynomials $\{P_n(t)\}_{n \geq 0}$ given by certain three term recurrence relations. (AU)

Scientific publications

(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)

RIBEIRO, LUANAL. SILVA; RANGA, A. SRI. A modified least squares method: Approximations on the unit circle and on (-1,1). Journal of Computational and Applied Mathematics, v. 410, p. 19-pg., 2022-08-15. (17/04358-8, 20/14244-2, 16/09906-0)

MARTINEZ-FINKELSHTEIN, A.; SILVA RIBEIRO, L. L.; SRI RANGA, A.; TYAGLOV, M.. COMPLEMENTARY ROMANOVSKI-ROUTH POLYNOMIALS: FROM ORTHOGONAL POLYNOMIALS ON THE UNIT CIRCLE TO COULOMB WAVE FUNCTIONS. Proceedings of the American Mathematical Society, v. 147, n. 6, p. 2625-2640, JUN 2019. (17/12324-6, 16/09906-0, 17/04358-8)

MARTINEZ-FINKELSHTEIN, A.; SILVA RIBEIR, L. L.; SRI RANGA, A.; TYAGLOV, M.. Complementary Romanovski-Routh Polynomials, Orthogonal Polynomials on the Unit Circle, and Extended Coulomb Wave Functions. Results in Mathematics, v. 75, n. 1, FEB 13 2020. (16/09906-0, 17/04358-8)

Academic Publications

(References retrieved automatically from State of São Paulo Research Institutions)

RIBEIRO, Luana de Lima Silva. Complementary Romanovski-Routh polynomials and functions with hybrid orthogonality. 2019. Doctoral Thesis - Universidade Estadual Paulista (Unesp). Instituto de Biociências Letras e Ciências Exatas. São José do Rio Preto São José do Rio Preto.