3.10 Proofs for Section 2.6.2 “Asymptotic Results as N→ ∞”
Lemma 3.10.1 Let be given by (2.184) with a(t) as in Assumption 2.4.5. It results that
Proof: Since a(t) has finite support [− 1/2, 1/2), to prove (3.155) is equivalent to prove that
Let us consider first the case .
Since a(t) is Riemann integrable (Assumption 2.4.5), we have
Let us consider now the case , ν > 0.
For every the function is Riemann integrable and we have
that is, ∀1 > 0 such that for ...