Orthogonal polynomials and related studies

• Grant number: 20/14244-2
• Support Opportunities: Regular Research Grants
• Start date: April 01, 2021
• End date: March 31, 2023
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Applied Mathematics
• Principal Investigator: Alagacone Sri Ranga
• Grantee: Alagacone Sri Ranga
• 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

Abstract

In recent years, however, studies of orthogonal polynomials on the unit circle had priority in the research activities of the member Alagacone Sri Ranga of gruPOSjrp. These polynomials are also commonly known as Szegö polynomials in honor of Gabor Szegö, who introduced them in the second half of the 20th century. Because of their applications in quadrature rules, signal processing, operator and spectral theory and many other topics, these polynomials have received a lot of attention in recent years. Orthogonal polynomials on the unit circle have been used by many mathematicians to obtain information about orthogonal polynomials defined on the real line. We have realized that the ideas behind the new techniques that we have used in our study of orthogonal polynomials on the unit circle can also be adopted to obtain new techniques to study orthogonal polynomials on the real line. Thus, carrying out these will be some of our priorities during next few years. Finally, as the most recent "work front" we will consider a study of Sobolev orthogonal polynomials involving pairs of measures on the real line. For these studies we will restrict the measures (within the pair) to satisfy a special condition. (AU)

Scientific publications

(6)

(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)

MARCATO, GUSTAVO; RANGA, A. SRI; LUN, YEN CHI. PARAMETERS OF A POSITIVE CHAIN SEQUENCE ASSOCIATED WITH ORTHOGONAL POLYNOMIALS. Proceedings of the American Mathematical Society, v. 150, n. 6, p. 15-pg., 2022-06-01. (20/14244-2, 16/09906-0)

MARCATO, G. A.; MARCELLAN, F.; RANGA, A. SRI; LUN, YEN CHI. Coherent pairs of measures of the second kind on the real line and Sobolev orthogonal polynomials. An application to a Jacobi case. STUDIES IN APPLIED MATHEMATICS, v. 151, n. 2, p. 34-pg., 2023-05-22. (20/14244-2)

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)

SUNI, M. HANCCO; MARCATO, G. A.; MARCELLAN, F.; RANGA, A. SRI. Coherent pairs of moment functionals of the second kind and associated orthogonal polynomials and Sobolev orthogonal polynomials. Journal of Mathematical Analysis and Applications, v. 525, n. 1, p. 32-pg., 2023-02-26. (20/14244-2)

SUNI, M. HANCCO; MARCELLAN, F.; RANGA, A. SRI. Pastro polynomials and Sobolev-type orthogonal polynomials on the unit circle based on a q-difference operator. JOURNAL OF DIFFERENCE EQUATIONS AND APPLICATIONS, v. 29, n. 3, p. 29-pg., 2023-04-12. (20/14244-2)

BRACCIALI, CLEONICE F.; DA SILVA, V, JESSICA; RANGA, A. SRI. A class of Sobolev orthogonal polynomials on the unit circle and associated continuous dual Hahn polynomials: Bounds, asymptotics and zeros. Journal of Approximation Theory, v. 268, AUG 2021. (20/14244-2, 16/09906-0)