Padé approximation for a multivariate Markov transform
Provides theoretical foundations for a multivariate generalization of the Stieltjes transform, relevant to spectral theory and approximation theory.
The authors characterize rationality of a multivariate Markov transform via Hankel determinants and derive a cubature formula for a special class of measures, extending classical results from spectral theory.
Methods of Padé 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.