CLOSED IDEALS OF THE ALGEBRA OF ABSOLUTELY CONVERGENT TAYLOR-SERIES

Let GAMMA be the unit circle, A(GAMMA) the Wiener algebra of continuous functions whose series of Fourier coefficients are absolutely convergent, and A+ the subalgebra of A(GAMMA) of functions whose negative coefficients are zero. If I is a closed ideal of A+ , we denote by S(I) the greatest common divisor of the inner factors of the nonzero elements of I and by I(A) the closed ideal generated by I in A(GAMMA). It was conjectured that the equality I(A) = S(I)H(infinity) and I(A) holds for every closed ideal I. We exhibit a large class F of perfect subsets of GAMMA, including the triadic Cantor set, such that the above equality holds whenever h(I) and GAMMA is-an-element-of F. We also give counterexamples to the conjecture.