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Quasi-projection operators with applications to differential-difference expansions

Author

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  • Costarelli, D.
  • Krivoshein, A.
  • Skopina, M.
  • Vinti, G.

Abstract

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.

Suggested Citation

  • Costarelli, D. & Krivoshein, A. & Skopina, M. & Vinti, G., 2019. "Quasi-projection operators with applications to differential-difference expansions," Applied Mathematics and Computation, Elsevier, vol. 363(C), pages 1-1.
    • Handle: RePEc:eee:apmaco:v:363:y:2019:i:c:31
    DOI: 10.1016/j.amc.2019.124623
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    References listed on IDEAS

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    1. Boucekkine, Raouf & Licandro, Omar & Paul, Christopher, 1997. "Differential-difference equations in economics: On the numerical solution of vintage capital growth models," Journal of Economic Dynamics and Control, Elsevier, vol. 21(2-3), pages 347-362.
    2. Asdrubali, Francesco & Baldinelli, Giorgio & Bianchi, Francesco & Costarelli, Danilo & Rotili, Antonella & Seracini, Marco & Vinti, Gianluca, 2018. "Detection of thermal bridges from thermographic images by means of image processing approximation algorithms," Applied Mathematics and Computation, Elsevier, vol. 317(C), pages 160-171.
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    1. Kolomoitsev, Yurii & Skopina, Maria, 2021. "Approximation by multivariate quasi-projection operators and Fourier multipliers," Applied Mathematics and Computation, Elsevier, vol. 400(C).

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