Abstract:
An arithmetical function f(x., ), r 2, with values in the field C of complex numbers is called here multi- additive, if (xi, yi) = 1, i= 1, 2, .... r imply xy) -f(x1 +, 5 (xi, yip , Q. In this paper, we first prove that the set (x, x7) of all multi-additive functions is a vector space over C. Next for disjoint sets (x);, xa, j, fxii, x' }of distinct arguments iv we prove, AOl ? _ _ cj) C — For a proper subset j, k}of the set [1, 2, r, } we construct certain H-homomorphisms Ht, j, k of ./1. (X into 1L (xv- )i) and prove that each H4, k can be decomposed uniquely to within order as the sum of certain irreducible 1-1-homomo-rphisms and then develop a theory of H-homomorphs i.e. H-subspaces of1L(xi, xd, x). 512.643 Matrices and linear mappings
Page(s):
15-28
DOI:
DOI not available
Published:
Journal: Punjab University Journal of Mathematics, Volume: 14-15, Issue: , Year: