HARMONIC ANALYSIS ON CERTAIN VECTOR SPACES.

Let 1 denote the vector space of all sequences of real numbers with the topology of coordinate-wise convergence. For 0 < p < infinity l sub p denote the subset of l consisting of all sequences x sub i which have the summation, from one to infinity of the (absolute value of x sub i) to the p power finite. The main efforts in the paper are to generalize Bochner's theorem and the Levy-continuity theorem to these l sub p spaces. (Author)