富氏变换反演公式的新证明

A NEW PROOF OF THE INVERSE FORMULA OF FOURIER TRANSFORM

富氏变换的反演公式应用极广 ,然而其经典证明很复杂 .本文借助非标准分析 (简记为NSA)提供一个简捷证明 .本文表明反演公式与富氏系数公式间存在着内在联系 .

The Inverse Formula of Fourier Transform has various applications, but the classical proof is tideously Complicated. A concise proof is given with the aid of Nonstandard Analysis. Meanwhile it shows the intrinsic relation between this inverse formula and that of the Fourier Coefficients.