The Moment Problem

First book to present a complete and unified treatment of all parts of the classical real moment problem (full and truncated, one-dimensional and multidimensional)
Develops classical and recent results with full proofs
Contains new results and concepts on the truncated multidimensional moment problem

Autorentext
Konrad Schmüdgen is professor at the University of Leipzig, Germany. He discovered the strict Positivstellensatz and developed in this manner the interplay between real algebraic geometry and moment problems. He obtained a number of fundamental results on full and truncated multidimensional moment problems.

Inhalt
Preface and Overview.- 1 Integral representations of linear functionals.- 2 Moment problems on abelian *-semigroups.- Part I The one dimensional moment problem.- 3 One dimensional moment problems on intervals: existence.- 4 One dimensional moment problems: determinacy.- 5 Orthogonal polynomials and Jacobi operators.- 6 The operator-theoretic approach to the Hamburger moment problem.- 7 The indeterminate Hamburger moment problem.- 8 The operator-theoretic approach to the Stieltjes moment problem.- Part II The one dimensional truncated moment problem.- 9 The one-dimensional truncated Hamburger and Stieltjes moment problems.- 10 The one-dimensional truncated moment problem on a bounded interval.- 11 The moment problem on the unit circle.- Part III The multidimensional moment problem.- 12 The moment problem on compact semi-algebraic sets.- 13 The moment problem on closed semi-algebraic sets: existence.- 14 The multidimensional moment problem: determinacy.- 15 The complex moment problem.- 16 Semidefinite programming and polynomial optimization.- Part IV The multidimensional truncated moment problem.- 17 Multidimensional truncated moment problems: existence criteria.- 18 Multidimensional truncated moment problems: basic concepts and special topics.- 19 The truncated moment problem for homogeneous polynomials.