Let A ≥ 1 and x1,...,xn ∈ [−A, A]. Show that, for any c > 0, L > 0, and 0                                     N1  δ,  TLf : f ∈ Ck(R) and  A −A |f(k) (x)| 2 dx ≤ c  , xn 1...

Let A ≥ 1 and x1,...,xn ∈ [−A, A]. Show that, for any c > 0, L > 0, and 0

                                    N1  δ,  TLf : f ∈ Ck(R) and

                                   ≤  c1 L δ (2A+2)c2( √c δ )1/k+c3

for some constants c1, c2, c3 ∈ R which only depend on k. Hint: Apply Lemma 20.4 on intervals [i, i + 1] with [i, i + 1] ∩ [−A, A] = ∅.