2020/02/02 by Yurii Kolomoitsev, Kolomoitsev, Yu., A. Krivoshein +3
Mathematics · #Mathematical Analysis and Transform Methods #Approximation Theory and Sequence Spaces #Mathematical Approximation and Integration
paper · pdf · doi:10.48550/arxiv.2002.00414
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 \widetildeφj. 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 \widetildeφj. 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.