Vanessa Avansini Botta Pirani

• XVII FCT Mathematics Symposium (XVII SMAT) and Regional Meeting of Applied and Computational Mathematics (ERMAC 2023), AO.R

• Abstract

  The main purpose of this research project is to show that self-reciprocal polynomials satisfy a three-term recurrence relation and they can be represented by a linear combination of Chebyshev polynomials of first kind. Furthermore, by known results of theory of orthogonal and para-orthogonal polynomials, we intend to explore properties of self-reciprocal polynomials, and to establish rel…

  Families of self-reciprocal polynomials with a three-term recurrence relation, AP.R

• Abstract

  This research project proposes the study of the main properties of the palindromic polynomials, with an special attention to the behavior of their zeros, which are symmetric with respect to not only the real line but also the unit circle. It will be studied recent results which establish conditions for all zeros of these polynomials to be located on the unit circle. In addition, it will…

  Location of zeros of polynomials in the unit disc: problems and challenges, AP.R

(Only some records are available in English at this moment)

• Abstract

  The main objective of this project is the study of the properties of Sobolev orthogonal polynomials on the real line, involving research into both general theory and that involving some special classes, such as Sobolev-Jacobi and Sobolev-Laguerre. Furthermore, we will consider the case in which the pair of related positive measures form a coherent pair of positive measures of the second …

  On Sobolev orthogonal polynomials on the real line, BP.MS

• Abstract

  This research project proposes to study the properties of orthogonal polynomialsin the real line, with the objective of inserting the candidate in the scientific research.Some classes of classical orthogonal polynomials will be studied (polynomials ofJacobi, Legendre, Chebyshev, Gegenbauer, Laguerre and Hermite) andsome of its applications, as in quadrature formulas. With this study, it i…

  Introduction to orthogonal polynomials, BP.IC

• Abstract

  The study of zeros of polynomial is a branch of mathematics that has a wide range of applications and also many open problems. In addition, it is a topic not fully addressed within the disciplines of most Mathematics Licentiate courses in Brazil. Therefore, it is intended that the candidate conduct a study on the behavior of zeros of polynomial, in general, so that she acquires a solid kn…

  Zeros of polynomials, BP.IC

(Only some records are available in English at this moment)

• Abstract

  The main objective of this project is to complement the candidate's training regarding the study of the properties of Sobolev orthogonal polynomials on the real line, where the pair of associated positive measures forms a coherent pair of positive measures of the second kind on the real line. The classes of Sobolev-Jacobi and Sobolev-Laguerre polynomials will be studied.

  Sobolev-Jacobi and Sobolev-Laguerre orthogonal polynomials, BE.EP.MS