23/11/2011, 16:15 — 17:15 — Room P3.10, Mathematics Building
Ana F. Loureiro, Centro de Matemática da Universidade do Porto
Polynomial sequences generated by integral powers of differential
operators
Polynomial sequences generated by integral powers of first and
second order differential operators conveniently chosen will be the
issue. More precisely, the focus will lie on their connection with
well known orthogonal polynomial sequences along with their
foremost structural properties. This talk will be split in two
parts. We will start by analysing the cases in which the
aforementioned differential operator is of first order, bringing
into analysis polynomial sequences associated to the classical
linear functionals of Hermite, Laguerre, Bessel and Jacobi.
Afterwards, the discussion will proceed towards the analysis of
polynomial sequences generated by second order differential
operators, which brings up the open problem of characterizing
orthogonal polynomial sequences with respect to certain positive
definite linear functionals. The Kontorovich-Lebedev transform and
the central factorial numbers will be an asset to attain our
goals.
References
- Ana F. Loureiro, New results on the Bochner condition about
classical orthogonal polynomials, J. Math An. Appl., 364 (2010)
307-323.
- Ana F. Loureiro, P. Maroni, S. Yakubovich, On a nonorthogonal
polynomial sequence associated with Bessel operator, Pre-Print CMUP
2011-10 (ArXiv:1104.4055v1)
- Ana F. Loureiro, S. Yakubovich, On a polynomial sequence
related to the Ditkin-Prudnikov problem, Pre-Print CMUP 2011-23
(arXiv:1110.6015v1)
