Along with his study of the
general Tauberian theorem in L1, N. Wiener introduced the algebra M1
which consists of all those continuous functions f on the real line R for
which
He proved that many features of L1, including the general Tauberian theorem, are
shared by M1. In this paper to generalize M1 to an arbitrary locally compact group
G. While doing this, a host of L1(G)-modules mutually related by conjugation and
the operation of forming multiplier modules. ℳ1(G) is among them. In case G is
abelian, ℳ1(G) is a Segal algebra, so that it has the same ideal-theoretical structure
as L1(G). If further G = R, ℳ1(G) reduces to the Wiener algebra M1 with an
equivalent norm.
![∞∑
xm∈a[nx,n+1]|f(x)| < ∞.
n= −∞](a180x.png)
