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Acta Mathematica Vietnamica

, Volume 43, Issue 2, pp 373–389 | Cite as

Quasi-interpolation Representation and Sampling Recovery of Multivariate Functions

  • Nguyen Manh Cuong
  • Mai Xuan Thao
Article
  • 51 Downloads

Abstract

In this paper, we prove a multivariate generalization of the quasi-interpolation representation of functions in Besov-type spaces by B-spline series with some equivalent discrete quasi-norms. Moreover, by using this representation, we construct linear sampling methods which give the asymptotic order of optimal linear sampling methods.

Keywords

Quasi-interpolation representation Besov-type spaces Linear sampling method Optimal recovery 

Mathematics Subject Classification (2010)

41A46 41A05 41A25 42C40 

Notes

Acknowledgements

This research is funded by the Vietnam National Foundation for Science and Technology Development (NAFOSTED) under Grant No. 102.01-2017.05.

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Copyright information

© Institute of Mathematics, Vietnam Academy of Science and Technology (VAST) and Springer Nature Singapore Pte Ltd. 2017

Authors and Affiliations

  1. 1.Department of Natural SciencesHong Duc UniversityThanh HoaVietnam

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