今日一言, 来自施瓦茨关于傅里叶级数与傅里叶积分的评价:
The theory of Fourier series and integrals has always had major difficulties and necessitated a large mathematical apparatus in dealing with questions of convergence. It engendered the development of methods of summation, although these did not lead to a completely satisfactory solution of the problem…. For the Fourier transform, the introduction of distributions (hence the space ) is inevitable either in an explicit or hidden form…. As a result one may obtain all that is desired from the point of view of the continuity and inversion of the Fourier transform.
傅里叶级数和傅里叶积分理论一直存在一些主要困难, 需要用到大量的数学工具以处理收敛性问题. 这一理论促进了求和方法的发展, 尽管这些方法并没有完全令人满意地解决这个问题… 而对于傅里叶变换, 我们不可避免的要引入分布(因此空间 ), 无论是显式的还是隐藏的形式… 而由此带来的结果就是, 人们可以从傅里叶变换的连续性和反演的角度获得他们所需的一切.*L. Schwartz*, 1950
