Chapter 12: The moment problem on compact semi-algebraic sets (revised version)

TL;DR

This chapter offers an improved, unified approach to the Archimedean Positivstellensätze for quadratic modules and semirings, along with new results on moment problems on compact semi-algebraic sets, based on recent research.

Contribution

It introduces a new unified framework for Positivstellensätze and extends moment problem results for semirings on compact semi-algebraic sets.

Findings

Unified approach to Archimedean Positivstellensätze

New results on Positivstellensätze for semirings

Enhanced understanding of moment problems on semi-algebraic sets

Abstract

The following is an improved version of Chapter 12 of my book [Sm17]. Among others, we present a new unified approach to the Archimedean Positivstellens\"atze for quadratic modules and semirings in Section 12.4 and we add a number of new results on Positivstellens\"atze for semirings and the corresponding moment problems.All references to formulas and to the bibliography of the book are retained. This version is essentially based on results from the recent paper [SmS23]. We will also use a result form book [Sm20].