The convergence properties of block-pulse series

Abstract

Abstract If the set of block-pulsa functions is incomplete, it cannot be guaranteed, for any given function, that an arbitrary small mean-square-error will be obtained by increasing the number of terms in the series. This paper studies the convergence properties of the block-pulse series. It is found that the set has a close relationship with delta sequences and it is proved that the set of block-pulse functions is in fact complete.