Multivariate determinates Mihai PutinarKonrad Schmuedgen 44A6032A2647B2514P0526E10moment problemdeterminacyintegral transform symmetric operatorquasi-analytic classspectral measuredisintegration The uniqueness question of the multivariate moment problem is studied by different methods: Hilbert space operators, complex function theory, polynomial approximation, disintegration, integral geometry. Most of the known results in the multi-dimensional case are reviewed and reproved, and a number of new determinacy criteria are developed. Indiana University Mathematics Journal 2008 text pdf 10.1512/iumj.2008.57.3692 10.1512/iumj.2008.57.3692 en Indiana Univ. Math. J. 57 (2008) 2931 - 2968 state-of-the-art mathematics http://iumj.org/access/