Moment computation in shift invariant spaces (Q1277070)

The paper is concerned with approximating the moments \(m_\beta(f)\) of a function \(f\in L^2({\mathbb R})\). In the first step one projects \(f\) into an \(h\)-shift invariant subspace \(S_h\) of \(L^2({\mathbb R})\). This subspace \(S_h\) is either a space spanned by \(h\)-translates of one function \(\phi\) or by \(h\)-translates of a finite set of functions. A recursion formula for the computation of \(m_\beta(f)\) for \(f\in S_h\) is derived in case that \(\phi\) generating \(S_h\) is refinable. An error estimate for the rate of convergence of the scheme is presented. The results are illustrated by some examples.