Norm approximation of periodic functions from noisy Fourier coefficients

Abstract

A new method of inverting the noisy Fourier transform of a periodic function is considered. Results concerning norm approximation in L P (T N ), 1 < p < -foo, or in C(T N ) where T^ is an N-dimensional torus are derived in a form suitable for applications. Then the method is tested by a numerical simulation procedure in the case of the space /^(T).