KWIM & RGA Seminar WS23/24: The Truncated Moment Problem on Unital Commutative Real Algebras
Mittwoch, 6. Dezember 2023
10 bis 11:30 Uhr
Prof. Salma Kuhlmann, Dr. Gabriela Michalek
Vortragende Person/Vortragende Personen:
Associate Professor Maria Infusino
Diese Veranstaltung ist Teil der Veranstaltungsreihe „KWIM Lecture Series“.
In this talk we investigate under which conditions a linear functional L defined on a linear proper subspace B of a unital commutative real algebra A admits an integral representation with respect to a nonnegative Radon measure supported on a prescribed closed subset K of the space of homomorphisms of A endowed with the weak topology. This is a generalization of the classical truncated moment problem and it has the advantage of encompassing also infinite dimensional instances, e.g. when A is not finitely generated and B is finite dimensional or when A is finitely generated and B infinite dimensional.
We first provide a criterion for the existence of such an integral representation for L in the case when A is equipped with a submultiplicative seminorm. Then we build on this result to prove a Riesz-Haviland type theorem, which also holds when A is not equipped with a topology. Beside infinite dimensional applications, this theorem extends some classical results for the truncated moment problem for polynomials in finitely many variables to situations when the monomial diagram associated to B contains infinitely many monomials in one of the variables, e.g. for rectangular or sparse truncated moment problems.
This is a joint work with Raúl Curto, Mehdi Ghasemi, and Salma Kuhlmann (http://www.mathjournals.org/jot/2023-090-001/2023-090-001-009.html )