摘要
Let K ∈ L1(R) and let f ∈ L∞(R) be two functions on R.The convolution(Kf)(x) =∫R K(x-y)f(y)dy can be considered as an average of f with weight defined by K.Wiener's Tauberian theorem says that under suitable conditions,if lim x→∞(K f)(x) = lim x→∞(K A)(x) for some constant A,then lim x→∞ f(x) = A.We prove the following-adic analogue of this theorem:Suppose K,F,G are perverse-adic sheaves on the affine line A over an algebraically closed field of characteristic p(p=l).Under suitable conditions,if(K F)|η∞≌(K G)|η∞,then F|η∞≌ G|η∞,where η∞ is the spectrum of the local field of A at ∞.
Let K ∈ L1(R) and let f ∈ L∞(R) be two functions on R.The convolution(Kf)(x) =∫R K(x-y)f(y)dy can be considered as an average of f with weight defined by K.Wiener’s Tauberian theorem says that under suitable conditions,if lim x→∞(K f)(x) = lim x→∞(K A)(x) for some constant A,then lim x→∞ f(x) = A.We prove the following-adic analogue of this theorem:Suppose K,F,G are perverse-adic sheaves on the affine line A over an algebraically closed field of characteristic p(p=l).Under suitable conditions,if(K F)|η∞≌(K G)|η∞,then F|η∞≌ G|η∞,where η∞ is the spectrum of the local field of A at ∞.
基金
supported by National Natural Science Foundation of China (Grant No.10525107)
