Abstract:
For Favard kernels, which are used to construct polynomials of best approximation for classes of periodic differentiable functions $W^r$, we obtain exact values of their norms as simple finite sums for odd $r$ and lower bounds for the norms for even $r$. Similar results are also obtained for the norms of the adjoint Favard kernels.
Keywords:Favard kernel, polynomial of best approximation, function class $W^r$, Favard sum, Kolmogorov width.