论文标题
Kotani的傅立叶变换定理
Kotani's Theorem for the Fourier Transform
论文作者
论文摘要
在1991年，Shinichi Kotani证明了一个定理，可以得出足够的条件，可以得出结论，$ f（x）$ on $ {\ mathbb z}^d $衰减，例如$ | x | x | x |^{ - （d-2）$ for $ x $的$ | x $，假设它的傅立叶fronScort $ \ hat f（k）$ | k） $ k $接近零。证据没有出版。根据Kotani未出版的证明，我们证明了Kotani定理的扩展。
In 1991, Shinichi Kotani proved a theorem giving a sufficient condition to conclude that a function $f(x)$ on ${\mathbb Z}^d$ decays like $|x|^{-(d-2)}$ for large $x$, assuming that its Fourier transform $\hat f(k)$ is such that $|k|^{2}\hat f(k)$ is well behaved for $k$ near zero. The proof was not published. We prove an extension of Kotani's Theorem, based on Kotani's unpublished proof.
