Harish-Chandra have got a Fourier inversion formula for C-c(infinity)(SL (2, R)). In this paper, we give a discussion on approximation identity kernels on SL(2, R) and get some properties of their Fourier transforms, ...Harish-Chandra have got a Fourier inversion formula for C-c(infinity)(SL (2, R)). In this paper, we give a discussion on approximation identity kernels on SL(2, R) and get some properties of their Fourier transforms, and then, making use of these properties and Harish-Chandra's result, we prove that the Fourier inversion formula obtained by Harish-Chandra is also valid for C-o(3)(SL,2, R)).展开更多
The sampling theorem on the real axis R was disscussed by many mathematician, a survey paper was given by P. L. Butzer (see[1]). The same kind theorem for Walsh transform was proved by Cheng Mingde. Shen Xiechang and ...The sampling theorem on the real axis R was disscussed by many mathematician, a survey paper was given by P. L. Butzer (see[1]). The same kind theorem for Walsh transform was proved by Cheng Mingde. Shen Xiechang and Zhou Mingqian in [4]. In [5], Li Shi-Xun established the sampling theorem on a kind of locally compact abelian groups, so extanded the two cases mentioned before. But the dual groups of the LCA groups which Li discussed was required to be compactly generated groups. In this paper, we proved the sampling theorem on the addition groups of p-series fields which do not have compactly generated dual groups.展开更多
文摘Harish-Chandra have got a Fourier inversion formula for C-c(infinity)(SL (2, R)). In this paper, we give a discussion on approximation identity kernels on SL(2, R) and get some properties of their Fourier transforms, and then, making use of these properties and Harish-Chandra's result, we prove that the Fourier inversion formula obtained by Harish-Chandra is also valid for C-o(3)(SL,2, R)).
文摘The sampling theorem on the real axis R was disscussed by many mathematician, a survey paper was given by P. L. Butzer (see[1]). The same kind theorem for Walsh transform was proved by Cheng Mingde. Shen Xiechang and Zhou Mingqian in [4]. In [5], Li Shi-Xun established the sampling theorem on a kind of locally compact abelian groups, so extanded the two cases mentioned before. But the dual groups of the LCA groups which Li discussed was required to be compactly generated groups. In this paper, we proved the sampling theorem on the addition groups of p-series fields which do not have compactly generated dual groups.
