Closed ideals of a regular Beurling algebra (Q1281295)

Let \(\Gamma\) be the unit circle in the complex plane and \(\omega\) a (submultiplicative) weight function on the integers. \(A_\omega(\Gamma)\) is the set of continuous functions on \(\Gamma\) with \(\sum\{|\widehat f(n)|\omega(n)< \infty: n\in\mathbb{Z}\}\) and \({\mathcal B}= \bigcap\{A_{\omega_k}(\Gamma): k\geq 1\}\), where \(\omega_k(n)\) is equal to \(e^{k\sqrt{|n|}}\) for negative \(n\) and \((n+ 1)^k\) for nonnegative \(n\). \({\mathcal B}\) is a superalgebra of \(A^\infty\), the set of \(C^\infty\) functions whose negative Fourier coefficients vanish. The author describes the dual of (as hyperfunctions) and the structure of its set of ideals, and obtains several ``division and approximation results''.