On a signed cosine equation ofN summands

Abstract

Summary. We find the set of continuous solutions f, g of the functional equation n=0where to = exp(27ri/N) and N • N. We show that if (f, g) # (0, 0) is a continuous solution of (I) then g satisfies the generalized cosine equation 'E,,v(co'z ).If g = go,0 = 1 then the space of continuous solutions f of (1) has dimension 2 and is spanned by z --, :? and z ~z N-1.

Functional equations and matrix-valued spherical functions

“…This functional equation occurs in Schmidt [25], Förg-Rob and Schwaiger [13] and Stetkaer [30,Theorem II.6], [31]. A signed functional equation related to (3.2), viz.…”

Functional equations involving means of functions on the complex plane

“…According to Proposition III.2 of [19] this implies that h N (z) = N−2 j=0 a j z j for some constants a 0 , . .…”

Some generalization of the quadratic and Wilson’s functional equation

“…Lukasik [8] showed the solution of the functional equation where (S, +) is an abelian semigroup, K is a finite subgroup of the automorphism group of S, (H, +) is an abelian group. where (G, +) is an abelian group, K is a finite subgroup of the automorphism group on G, f, g, h : G → C, was studied by Förg-Rob and Schwaiger [5], Gajda [6], Stetkaer [11,12], Badora [2].…”