Estimates for the Lebesgue functions and the Nevai formula for the $sinc$-approximations of continuous functions on an interval

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.