A variant of the Hausdorff theorem for multiindex matrices I Original Research Article

An infinite matrix is regular if it is a limit preserving transformation in the domain of convergent sequences. A classical Hausdorff theorem states that some matrices composed of diagonal matrices and matrices, whose elements are defined as alternating Newton symbols, are regular iff the diagonal elements of the above diagonal matrices are consecutive moments of a Stieltjes integral. In this paper an analogous theorem for multiindex infinite matrices is proved.