Wednesday, November 8, 2017 - 17:00 in V3-201
An infinite dimensional umbral calculus
A talk in the Bielefeld Stochastic Afternoon series by
Maria J. Oliveira from Universidade Aberta, University of Lisbon
| Abstract: |
In its modern form, umbral calculus is a study of shift-invariant linear operators acting on polynomials, their associated polynomial systems of binomial type and Sheffer sequences. In this talk we present an extension of this calculus to the infinite dimensional space of distributions on $\mathbb{R}^d$, $d\in\mathbb{N}$. A procedure for lifting polynomials on $\mathbb{R}$ to polynomials on the space of distributions on $\mathbb{R}^d$ is discussed as well. Using this procedure we recover, in particular, the Hermite polynomials, the Charlier polynomials, the orthogonal Laguerre polynomials, well-known in different branches of infinite dimensional analysis.
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