Hölder classes of vector-valued functions and convergence of the best predictor

AbstractThe Hölder classes Λa of vector-valued functions are defined. The functions in each space Λa are completely characterized by conditions concerning the decay of their Fourier coefficients, their smoothness, and their approximability by polynomials. It is shown that, in some sense, Λa is closed under multiplication, inversion, and factorization. These ideas are applied to a prediction problem for multivariate stationary processes. Specifically, spectral criteria are derived for the convergence rate of the series representation for the best linear predictor