Orador: Maria das Neves Rebocho (Departamento de Matemática, UBI). Data, hora e local: 19 de Junho de 2014, início às 15h na sala de reuniões do Departamento de Matemática.
Resumo: A sequence of orthogonal polynomials on the real line (OPRL), say , is said to be Laguerre-Hahn if the corresponding Stieltjes function, , satisfies a Riccati type differential equation with polynomial coeficients
As particular cases, some well-known families of orthogonal polynomials are obtained: the semi-classical OPRL, when ; the classical OPRL (Hermite, Laguerre, Jacobi), when and , , .
In this talk we focus on the following problem: given a time dependence on the polynomials of (1), to describe the deformations of the three-term recurrence relation coefficients of . Such deformations are described by nonlinear (difference in and differential in ) equations. We deduce discrete Lax equations which lead to difference equations for the corresponding three term recurrence relation coefficients, and we analyze the continuous -differential equations.
Seminário realizado com o apoio do Centro de Matemática – 212 (Pest-OE/MAT/UI0212/2014).