A large class of multivariate quasi-projection operators is studied. These operators are sampling-type expansions ∑k∈Zdck(f)ψ(Aj·−k), where A is a matrix and the coefficients ck(f) are associated with a tempered distribution ψ˜. Error estimates in Lp-norm, 2 ≤ p < ∞, are obtained under the so-called weak compatibility conditions for ψ˜ and ψ, and the Strang-Fix conditions for ψ. Approximation order depends on the smoothness of f and on the order of the compatibility and the Strang-Fix conditions. A number of examples aimed at engineering applications are provided. A special attention is payed to the quasi-projection operators associated with differential-difference expansions. Applications to solving some differential-difference equations are presented.
CITATION STYLE
Costarelli, D., Krivoshein, A., Skopina, M., & Vinti, G. (2019). Quasi-projection operators with applications to differential-difference expansions. Applied Mathematics and Computation, 363. https://doi.org/10.1016/j.amc.2019.124623
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