Dear all,

we are pleased to invite you to the two seminars organised by the Department of Statistical Sciences, Sapienza University of Rome, which can be followed via Zoom.

*Location:* Room n.24, 4th floor, Edificio CU002 (Scienze Statistiche) *Zoom: * https://uniroma1.zoom.us/j/84380852385?pwd=RDBrcVdvelRMM0VmczlXYWgwL2pPZz09

*Time:* *Monday 23th of October, at 10.30* *Speaker: *Josè Luis Da Silva (University of Madeira - Portugal) *Title:* A Biorthogonal Approach to Infinite Dimensional Fractional Poisson Measures

*Abstract*: We use a biorthogonal approach to the analysis of the infinite dimensional fractional Poisson measure. The complex Hilbert space w.r.t. these measures are described in terms of a proper system of generalized Appell polynomials. The kernels of the monomials may be expressed in terms of the Stirling operators of the first and second kind as well as the falling factorials in infinite dimensions. Associated to this system of Appell polynomials is the dual Appell system which is suitable to describe generalised functions. We then construct and characterize test and generalised functions in terms of integral transform as entire functions.

*Time:* *Tuesday 24th of October, at 14.30* *Speaker: *Tobias Kuna (University of L'Aquila) *Title:* An Intrinsic Characterization of Moment Functionals in the Compact Case

*Abstract:* We discuss characterizations of linear functionals $L$ on an unital commutative real algebra $A$ which can be represented as integral w.r.t. a compactly supported Radon measure on the character space of $A$. We give a characterization by the following three types of conditions: bounds on the growth of $(L(a^n))_n$, non-negativity of $L$ on Archimedean quadratic models, and continuity of $L$ w.r.t. submultiplicative seminorms on $A$. We will relate each of these conditions to a different technique solving this instance of the moment problem. Surprisingly, we can also provide an exact characterization of the compact support of the representing Radon measure purely in terms of $L$. This is a joint work arXiv:2204.05630 with Maria Infusino, Salma Kuhlmann and Patrick Michalski.

Best regards. Luisa Beghin

*************************************************************** Luisa Beghin Dipartimento di Scienze Statistiche Fac. Ingegneria dell'Informazione, Informatica e Statistica "SAPIENZA" Università di Roma Piazzale Aldo Moro 5, 00185 Roma T (+39) 06 49910543 F (+39) 06 4959241 https://sites.google.com/site/luisabeghin/ *****************************************************************