超函数

示例

• ${\displaystyle f}$为复平面上的任一全纯函数，${\displaystyle f}$在实轴上可表示为超函数${\displaystyle (f,0)}$${\displaystyle (0,-f)}$
• 单位阶跃函数可表示为超函数${\displaystyle H(x)=\left({\frac {1}{2\pi i}}\log(z),{\frac {1}{2\pi i}}\log(z)-1\right)}$
• 狄拉克δ函数可表示为超函数${\displaystyle \left({\frac {1}{2\pi iz}},{\frac {1}{2\pi iz}}\right)}$

参考文献

• Hörmander, Lars, The analysis of linear partial differential operators, Volume I: Distribution theory and Fourier analysis, Berlin: Springer-Verlag, 2003, ISBN 3-540-00662-1.
• Sato, Mikio, Theory of Hyperfunctions, I, Journal of the Faculty of Science, University of Tokyo. Sect. 1, Mathematics, astronomy, physics, chemistry, 1959, 8 (1): 139–193, MR 0114124.
• Sato, Mikio, Theory of Hyperfunctions, II, Journal of the Faculty of Science, University of Tokyo. Sect. 1, Mathematics, astronomy, physics, chemistry, 1960, 8 (2): 387–437, MR 0132392.