Interpolating sets for spaces of functions with derivatives in the Wiener algebra

Let p be a non-negative integer. We set A(p) (T) = {f is an element of C(T), Sigma(nis an element ofZ) \(f) over cap (n)\ \n\(p) < + infinity} and A(p)(+)(T) = {f is an element of A(p)(T) : (f) over cap (n) = 0, n < 0}, where C(T) is the space of continuous functions on the unit circle T. A closed subset E of T is said to be an interpolating set of order p for A(p)(T), if for every function f is an element of A(p)(T), there exists g is an element of A(p)(+)(T) such that f((k))(z) = g((k))(z), z is an element of E, 0 less than or equal to k less than or equal to p. We prove that the perfect symmetric set E-xi = {exp(2ipi (1 - xi)Sigma(k=1)(+infinity)epsilon(k)xi(k-1)), epsilon(k) = 0 or 1} of constant ratio xi is an element of (0, 1/2), is an interpolating set of order p for A(p)(T) if and only if 1/xi is a Pisot number.