Geodesic
A criterion for the uniform convergence of sinc-approximations on a segment
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 6 (2008), pp. 66-78

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In this paper we obtain a criterion for the uniform convergence inside the interval $(0,\pi)$ of values of E. T. Whittaker operators $$ L_n(f,x)=\sum_{k=0}^{n}\frac{\sin(nx-k\pi)}{nx-k\pi}f\biggl(\frac{k\pi}{n}\biggr) $$ for continuous functions. This criterion is similar to that of A. A. Privalov for the convergence of interpolation Lagrange–Chebyshev polynomials and trigonometric ones.
Keywords: cardinal function, sinc approximation, convergence; criterion of the uniform convergence, cardinal function, approximation
Mots-clés : Lagrange interpolation, interpolation process. 
@article{IVM_2008_6_a6,
     author = {A. Yu. Trynin},
     title = {A criterion for the uniform convergence of sinc-approximations on a segment},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {66--78},
     publisher = {mathdoc},
     number = {6},
     year = {2008},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2008_6_a6/}
}
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A. Yu. Trynin. A criterion for the uniform convergence of sinc-approximations on a segment. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 6 (2008), pp. 66-78. http://geodesic.mathdoc.fr/item/IVM_2008_6_a6/