A variant of the Hausdorff theorem for multiindex matrices. I (Q1124919)

The main task of this work is to generalize a well-known result of Toeplitz for regularity to fit mutiindex matrices. Thereby this enables one to classify regularity for Hausdorff multiindex matrices. The author begins with a proof of the 3-index matrices case for the generalized Toeplitz theorem. The proof is long and tedious similar to the technique of gliding hump. One hence may expect somehow a shorter proof can be found perhaps with the aid of functional analysis theory.