Approximation in a Class of Banach Algebras of Quasianalytically Smooth Analytic Functions

We investigate the structure of primary ideals at infinity in spaces of bounded analytic functions in the lower half-plane, having a specified degree of smoothness on the real line (varying from very low to quasianalytic). The problem is related to classical works of Wiener and Beurling. A new method is introduced which permits us to treat both the non-quasianalytic and the quasianalytic cases; previous methods could only handle the non-quasianalytic case. C