Dan Chazan, Alan G. Konheim, et al.
Journal of Combinatorial Theory
Let G be a locally compact abelian group and B+(G) the family of continuous, complex-valued non-negative definite functions on G. Set A complex-valued function defined on the open unit disk is said to operate on {B+1(G), B+(G)} if fϵB+(G) implies F(f)ϵB+(G), similarly for {ϕ(G),ϕ(G)}. Recently C. S. Herz has given a proof of a conjecture of W. Rudin that F operates on {B+1(G), B+(G)} if and only if for a certain class of G. We shall show by independent methods that F operates on ϕ(R1) if F is given by (*) for |z| ≦ 1 and F(1)〝 1. This answers a question posed by E. Lukacs and provides in addition an alternate proof of Herz’s theorem. © 1965 by Pacific Journal of Mathematics.
Dan Chazan, Alan G. Konheim, et al.
Journal of Combinatorial Theory
Roy L. Adler, Benjamin Weiss
Israel Journal of Mathematics
Alan G. Konheim, Martin Reiser
Journal of the ACM
William H. Burge, Alan G. Konheim
Journal of the ACM