摘要
用(S’(R^n))~2n表示2n个S’(R^n)的列笛卡尔积.对S’(R^n)上的连续线性算子K,用同一记号表示由它诱导出的(S’(R^n))~2n上如下定义的连续线性算子:
It is proved that for each 2nx2n symplectic matrix S, there exists con-tinuous linear map Fs: S'(Rn)→S'(Rn), unique up to a constant factor, such thatFs is called the generalized Fourier transformation. Some properties and applica-tions of Fs are obtained. In especial , the lower and upper boundedness of Fs in Hm(Rn) is proved and a new proof of L. Hormander Theorem is given.
基金
国家青年科学基金资助
