ACL Workshop Dialogues in Infinite Dimensional Analysis | Public Talks #1
   29 de Setembro - 11 horas
ACL workshop "Dialogues in Infinite Dimensional Analysis“ will take place online via zoom (please find below the access data) from the coming Tuesday (September 29) to Thursday (October, 1st). On each day there will be a public talk (including questions and answers) from 11:00-12:00, Lisbon time (i.e.12:00-13:00 in Berlin and Paris). The titles and abstracts can be found below. Organizers: Wolfgang Bock (TUK), Rui Vilela Mendes (ACL), Maria João Oliveira (UAb), Ludwig Streit (ACL/BIBOS).

Speaker: Eugene Lytvynov, Swansea University, UK

Time: Tuesday, September 29, 2020, 11am Lisbon Time

Title: An infinite dimensional umbral calculus -- algebraic and analytic aspects

Abstract: The classical umbral calculus studies Sheffer polynomial sequences (including polynomial sequences of binomial type and Appell sequences) and related operators. In this talk, we will develop foundations of umbral calculus on the space $\mathcal D'$ of distributions on $\mathbb R^d$, whichleads to a general theory of Sheffer polynomial sequences on $\mathcal D'$. We will construct a lifting of a Sheffer sequence on $\mathbb R$ to a Sheffer sequence on $\mathcal D'$. Examples of lifted polynomial sequences include the falling and rising factorials, Abel, Hermite, Charlier, and Laguerre polynomials on $\mathcal D'$. Some of these polynomials have already appeared in different branches of infinite dimensional (stochastic) analysis and played there a fundamental role. We will also study extensions of Sheffer operators (including umbral operators) to linear homeomorphisms on spaces of entire functions on $\mathcal D'_{\mathbb C}$, the complexification of $\mathcal D'$. Our results here extend the well known internal descriptions of the test spaces for Hida and Kondratiev distributions, respectively. The talk is based on joint papers with Dmitri Finkelshtein, Yuri Kondratiev, Maria Jo\~{a}o Oliveira, and Ludwig Streit.

Join Zoom Meeting:

Meeting ID: 893 8376 8418

Passcode: 393934