The asymptotic representations on the norm of the Fourier operators ✩

In this paper by a new method we first get π 0 |sin t | t dt = 2 π ln n + C + O(n−2). Based on it, we then obtain a new asymptotic representation on the norm Ln of the Fourier operators as follows: Ln = 4 π2 ln n +C∗ + O(n−1).  2004 Elsevier Inc. All rights reserved.