On basicity of exponentials in \(L^ p(d\mu)\) and general prediction problems (Q1314902)

Usually in prediction theory the state space is similar with a subspace \(M\) spanned by a set of exponential functions with given frequencies. Therefore some informations about \(M\) have reflections in the corresponding prediction. Here, for a nonnegative measure which is absolutely continuous with respect to the normalized Lebesgue measure \(dm\) on the unit torus, a description of the annihilator space \(M^\perp\) is given. This permits reducing the general prediction problem related to \(M\) to an easier one related to \(M^\perp\).