Remarks on properties of probability distributions determined by conditional moments (Q1092557)

In this paper we consider some properties of rotation-invariant distributions on \(R^ n\), which are determined by a form of conditional moment of order \(\alpha >0\). In particular we prove that the Gaussian distribution is determined uniquely by its conditional moments and we investigate the related question of finiteness of exponential moments. The case of general \(\alpha >0\) appears to be more difficult to analyze than the case \(\alpha =2\), studied previously by other authors.