Approximation properties of periodic quasi-projection operators with matrix dilations are studied. Such operators are generated by a sequence of functions φj and a sequence of distributions/functions φ˜j. Error estimates for sampling-type quasi-projection operators are obtained under the periodic Strang-Fix conditions for φj and the compatibility conditions for φj and φ˜j. These estimates are given in terms of the Fourier coefficients of approximated functions and provide analogs of some known non-periodic results. Under some additional assumptions error estimates are given in other terms in particular using the best approximation. A number of examples are provided.
Scopus subject areas
- Applied Mathematics