Bezalel Gavish, Alan G. Konheim
IEEE Transactions on Communications
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.
Bezalel Gavish, Alan G. Konheim
IEEE Transactions on Communications
Alan G. Konheim, Willard L. Miranker
Mathematics of Computation
Roy L. Adler, L.Wayne Goodwyn, et al.
Israel Journal of Mathematics
Alan G. Konheim
IEEE Transactions on Communications