  Methods of Pad\'e approximation are used to analyse a multivariate Markov
transform which has been recently introduced by the authors, and which is
generalizing the well-known in Spectral theory Stieltjes transform (Markov
function) of one-dimensional measure. The first main result is a
characterization of the rationality of the Markov transform via Hankel
determinants. The second main result is a cubature formula for a special class
of measures.
