Infinite dimensional moment problem: open questions and applications

Infinite dimensional moment problems have a long history in diverse applied areas dealing with the analysis of complex systems but progress is hindered by the lack of a general understanding of the mathematical structure behind them. Therefore, such problems have recently got great attention in real algebraic geometry also because of their deep connection to the finite dimensional case. In particular, our most recent collaboration with Murray Marshall and Mehdi Ghasemi about the infinite dimensional moment problem on symmetric algebras of locally convex spaces revealed intriguing questions and relations between real algebraic geometry, functional and harmonic analysis. Motivated by this promising interaction, the principal goal of this paper is to identify the main current challenges in the theory of the infinite dimensional moment problem and to highlight their impact in applied areas. The last advances achieved in this emerging field and briefly reviewed throughout this paper led us to several open questions which we outline here.Comment: 14 pages, minor revisions according to referee's comments, updated reference

From Survivor to Advocate: The Therapeutic Benefits of Public Disclosure

This study examined the therapeutic impact of public disclosure for survivors of sexual assault. The purpose was to identify how disclosure in a public setting affected the recovery process of survivors of sexual assault. Three adult women were interviewed about their experiences. This study analyzed the meaning of public disclosure for these women in order to understand if it had therapeutic value in their recoveries. Each woman indicated that public disclosure helped strengthen her recovery. Public disclosure helped these women connect with other survivors and supporters, which assisted in alleviating feelings of shame. There is a need to study public disclosure for survivors of sexual assault further, but this study found that it can be helpful during recovery

The full infinite dimensional moment problem on symmetric algebras of locally convex real spaces

This talk aims to introduce an infinite dimensional version of the classical full moment problem and explore certain instances which actually arise in several applied fields. The general theoretical question addressed is whether a linear functional $L$ on the symmetric algebra $S(V)$ of a locally convex topological real vector space $V$ can be represented as an integral w.r.t.\! a non-negative Radon measure supported on a fixed subset of the algebraic dual $V^*$ of $V$. I present a recent joint work with M. Ghasemi, S. Kuhlmann and M. Marshall where we get representations of continuous positive semidefinite linear functionals $L: S(V)\rightarrow \mathbb{R}$ as integrals w.r.t.\! uniquely determined Radon measures supported in special sorts of closed balls in the topological dual space $V\u27$ of $V$. A better characterization of the support is obtained when $L$ is positive on a $2d-$power module of $S(V)$. I compare these results with the corresponding ones for the full moment problem on locally convex nuclear spaces, pointing out the crucial roles played by the continuity and the quasi-analyticity assumptions on $L$ in determining the support of the representing measure. In particular, I focus on a joint work with T. Kuna and A. Rota where we derive an analogous result for functionals on the symmetric algebra of the space of test functions on $\mathbb{R}^d$ which are positive on quadratic modules but not necessarily continuous. This setting is indeed general enough to encompass many spaces which occur in concrete applications, e.g.\! the space of point configurations

Junior Recital: Christina Infusino, soprano

Kennesaw State University School of Music presents Junior Recital: Christina Infusino, soprano.https://digitalcommons.kennesaw.edu/musicprograms/1866/thumbnail.jp