Abstract:
We obtain some upper and lower estimates for the sequences of the Lebesgue functions and constants of the Whittaker operators
\begin{equation*}
L_n(f,x)=\sum^n_{k=0}\frac{\sin(nx-k\pi)}{nx-k\pi}f\biggl(\frac{k\pi}n\biggr)
\end{equation*}
for continuous functions. We give an analog of Nevai's formula for the Lagrange–Chebyshev and Lagrange–Laguerre interpolation polynomials for the operators under consideration. Its “local” version is established.
Keywords:approximation of continuous functions, Lagrange interpolation, uniform convergence.
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