Date:
2012..02..28
Event:
Seminario Departamento de Física y Matemáticas
Venue:
Universidad de Alcalá, Spain
Abstract
We present on the one hand algebraic and differential/difference properties for semiclassical-Sobolev polynomial, which are orthogonal with respect to the inner product \[ \left\langle p, r \right\rangle _S=\left\langle {{\bf u}} ,{p\, r}\right \rangle +\lambda \left \langle {{\bf u}}, {{\mathscr D}p \,{\mathscr D}r}\right\rangle, \] where \(\bf u\) is a semiclassical linear functional, \(\mathscr D\) is the differential (or the difference or the \(q\)-difference, respectively) operator, and \(\lambda\) is a positive constant; as well as algebraic relations between them and the polynomial sequence orthogonal with respect to the semiclassical functional \(\bf u\). And on the other hand we present a degenerate version of the Favard's Theorem which is valid for all sequences of polynomials satisfying a three-term recurrence relation \[ xp_n=\alpha_n p_{n+1}+\beta p_n+\gamma_n p_{n-1}, \] even when some coefficient \(\gamma_n\) vanishes, i.e., the set \(\{n:\gamma_n=0\}\ne \emptyset\).Download
| Link | Size | Description |
|---|---|---|
| seminar_16.pdf | 660 KB | Slides (PDF, 34 pages, 24 slides) |