Wiener Algebra

Suppose W is the set of all complex-valued functions f on the interval [0,2pi] of the form

for t in [0,2pi], where the alpha_k in C and sum_(k=-infty)^(infty)|alpha_k|<infty. The set W with the usual pointwise operations and with the norm

is a commutative Banach algebra and is called the Wiener algebra.

There is an isometric isomorphism between l^1(Z) and W given by f->f^~, where

with t in [0,2pi].

This entry contributed by Mohammad Sal Moslehian

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Moslehian, Mohammad Sal. "Wiener Algebra." From MathWorld--A Wolfram Resource, created by Eric W. Weisstein. https://mathworld.wolfram.com/WienerAlgebra.html

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