Closed Ideals In Banach Algebra (?)∩ A(D)of Analytic Functions

In this paper, we study closed ideals of Banach algebra D ∩ A(D) of analytic functions and D is the Dirichlet space, A(D) is the disc algebra. Let U be an inner function, E be a closed subset of T which satisfy certain conditions. Let I(U, E) be the set of functions in D ∩ A(D) which inner part are divisible by U and which vanish on E. Then I(U, E) is a closed ideal of D ∩ A(D). Moreover, we prove that ideals of finite codimension of D ∩ A(D) is obtained in this manner. Thus, we obtain a complete description of ideals of finite codimension of algebra D ∩ A(D).