Poisson measure as a spectral measure of a family of commuting selfadjoint operators, connected with some moment problem

TL;DR

This paper demonstrates that the Poisson measure serves as a spectral measure for a family of commuting selfadjoint operators linked to a generalized moment problem, expanding understanding of spectral measures in operator theory.

Contribution

It introduces a novel connection between the Poisson measure and spectral measures of commuting selfadjoint operators related to a generalized moment problem.

Findings

Poisson measure is a spectral measure for certain commuting operators

Establishes a link between Poisson measure and a generalized moment problem

Expands the framework of spectral measures in operator theory

Abstract

It is proved that the Poisson measure is a spectral measure of some family of commuting selfadjoint operators acting on a space constructed from some generalization of the moment problem.