_{} Fourier transforms on locally compact unimodular groups
_{} Fourier transforms on locally compact unimodular groups
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DOI：
10.1090/s0002-9947-1958-0100235-1
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发表时间：
1958-02
影响因子：
1.3
通讯作者：
R. Kunze
中科院分区：
文献类型：
--
作者：
R. Kunze
f（x）= f gx（a）f（a）da给出的g的acter g组g;当F在L1（G）NL2（G）中时，T：F-> F是一个等距映射到L2（G）中，可以将其扩展到具有L2（G）的L2（G）等轴测图。此外，L2（g）中卷积BYF的操作通过t与乘法相等，在L2（g）中通过f乘以MP。实际上MF = TLFT-1。如果G是ABELIAN，则使用L2（G）中的任何封闭的密集定义的操作员，其与组翻译的通勤通过T等于L2（G）中的乘法，这通过G（Segal [4]）上的可测量函数。特别是，如果F在Abelian G组G和LF上可以测量F，则用TLFT-1 = M密集定义F，则自然称F f fourier f transe f的傅立叶变换。由于F和MP本质上是等效的，因此定义傅立叶是有意义的
acter group G of G given by F(X) =f Gx(a)f(a)da; when f is in L1(G)nL2(G), T: f->F is an isometric map into L2(G) which can be extended to an isometry of L2(G) with L2(G). Moreover the operation Lf of convolution byf in L2(G) is unitarily equivalent via T to multiplication, Mp by F in L2(G). In fact MF= TLfT-1. If G is abelian, any closed densely defined operator in L2(G) which commutes with the group translations is equivalent via T to a multiplication in L2(G) by a measurable function on G, (Segal [4]). In particular if f is measurable on the abelian group G and Lf is closed and densely defined with TLfT-1 = M it is natural to call F the Fourier transform of f. Since F and MP are essentially equivalent it makes sense to define the Fourier