Corpus ID: 235457993

On the stability of the L2 projection and the quasiinterpolant in the space of smooth periodic splines

@article{Dougalis2021OnTS,
  title={On the stability of the L2 projection and the quasiinterpolant in the space of smooth periodic splines},
  author={D. A. Dougalis},
  journal={ArXiv},
  year={2021},
  volume={abs/2106.09060}
}
In this paper we derive stability estimates in Land L∞based Sobolev spaces for the L projection and a family of quasiinterolants in the space of smooth, 1-periodic, polynomial splines defined on a uniform mesh in [0, 1]. As a result of the assumed periodicity and the uniform mesh, cyclic matrix techniques and suitable decay estimates of the elements of the inverse of a Gram matrix associated with the standard basis of the space of splines, are used to establish the stability results. 
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