Corpus ID: 55275563

Approximation of classes of analytic functions by de la Vallee Poussin sums in uniform metric

@article{Serdyuk2011ApproximationOC,
  title={Approximation of classes of analytic functions by de la Vallee Poussin sums in uniform metric},
  author={A. Serdyuk and Ie. Yu. Ovsii and A. Musienko},
  journal={arXiv: Classical Analysis and ODEs},
  year={2011}
}
In this paper asymptotic equalities are found for the least upper bounds of deviations in the uniform metric of de la Vallee Poussin sums on classes of 2\pi-periodic (\psi,\beta)-differentiable functions admitting an analytic continuation into the given strip of the complex plane. As a consequence, asymptotic equalities are obtained on classes of convolutions of periodic functions generated by the Neumann kernel and the polyharmonic Poisson kernel. 
8 Citations

References

SHOWING 1-10 OF 30 REFERENCES
Approximation of Classes of Analytic Functions by de la Vallée-Poussin Sums
  • 13
  • Highly Influential
Approximation of Classes of Analytic Functions by Fourier Sums in Uniform Metric
  • 12
Approximation of Poisson integrals by de la Valleé-Poussin sums in uniform and integral metrics
  • 6
Approximation of Analytic Periodic Functions by de la Vallée-Poussin Sums
  • 9
Approximation of Poisson Integrals by de la Vallée Poussin Sums
  • 9
Asymptotic behavior of best approximations of classes of Poisson integrals of functions from Hω
  • 5
  • PDF
Approximation by fourier sums and best approximations on classes of analytic functions
  • 15
Methods of Approximation Theory
  • 108
Exact Constants in Approximation Theory
  • 252
...
1
2
3
...