Beste Approximation von Elementen eines nuklearen Raumes

We show that
$$ |f(x)-V_{n,m}(f,x)|\leqslant\frac C{m+1}\sum^n_{k=n-m}E_k\left[1+\ln\left(1+\frac{n-m}{k-n+m+1}\right)\right], $$
for every continuous function with period $2M$, where $C$ is an absolute constant and $0\le m\le n$, and we then apply this bound.