Differentiation of Fourier Series via Orthogonal Derivative

@article{CruzSantiago2015DifferentiationOF,
  title={Differentiation of Fourier Series via Orthogonal Derivative},
  author={Rene Cruz-Santiago and Jos{\'e} L. L{\'o}pez-Bonilla and R. L{\'o}pez-V{\'a}zquez},
  journal={Journal of the Institute of Science and Technology},
  year={2015},
  volume={20},
  pages={113-114}
}
It is very known that if the operator d/dx acts on each term into a convergent Fourier Series (FS), then it may result a divergent series. This situation is remedied applying the symmetric derivative to FS, which implies the existence of the important Fejer-Lanczos Factors. In this paper, we show that the orthogonal derivative also leads to these Factors. Journal of Institute of Science and Technology, 2015, 20(2): 113-114 
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2 Citations

2 Citations

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Citation Type

Differentiation of a Fourier series
It is very known that if the operator acts on each term into a convergent Fourier series (FS) then it may result a divergent series. This situation is remedied applying the symmetric derivative to…
An Inequality for the Fejér-Lanczos Factors
We find, via numerical experimentation, an inequality satisfied by the Fejer-Lanczos factors. Let’s remember that those factors are important for a correct differentiation of Fourier series.

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