Abstract
I Results and comments The object of this paper is to carry out proofs of weighted versions of Wiener type inversion theorems in the theory of Banach algebras and to derive, as an application, inversion theorems for multiplicative arithmetical functions. Such theorems using general weight functions do not seem to have been known or stated explicitly, until now. For D=2~ or D = N u {0}, denote by W(D) the set of positive valued weight functions (~) on D satisfying (1) cn(0)=l, o(m+n)<co(m)~o(n) for all m, neD and
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