论文标题
准中心功能和局部因素
Quasi-inner functions and local factors
论文作者
论文摘要
我们介绍了{\ it quasi-inner}的概念，并证明产品$ u =ρ_\ infty \ prodρ_v$的$ m+1 $ 1 $比率的本地{$ l $ - }因子{$ρ_v（z）=γ_v（z）/γ_v（z）/γ_v（1- z）$} Archimedean plote是{Quasi-inner}的左侧$ \ re（z）= \ frac 12 $的{quasi-inner}。 OFF对角部分$ U_ {21} $在Hilbert Space的正交分解中乘以$ U $的矩阵$ u $ l^2 $ l^2 $ l^2 $的正方形集成功能，进入Hardy Space $ h^2 $及其正交补充的关键线上是一个压缩操作员。当在单位磁盘上解释时，准内部条件意味着相关的Haenkel矩阵是紧凑的。我们表明，没有一个单独的非一切级非公共比率$ρ_v$是准inner，为了证明我们的主要结果，我们使用高斯乘法定理来考虑Archimedean Ratio $ρ_\ infty $ to $ m $ m $ m $ quasi-inner函数，其产品具有每种$ρ_v$ρ_V$ with the Quasi-Inner的产品。最后，我们证明了Sonin的空间仅仅是对角部分的内核$ u_ {22} $的准inner函数$ u =ρ_\ infty $，而当$ u（f）= \ prod_ {v \ in f}ρ_V$ in Indive and thery thery thery thery Indive thery thery thery thery thery thery thery thery thery thery tho tho tho tho prod_ {v \ （经典）Sonin空间的半本地类似物。
We introduce the notion of {\it quasi-inner} function and show that the product $u=ρ_\infty\prod ρ_v$ of $m+1$ ratios of local {$L$-}factors {$ρ_v(z)=γ_v(z)/γ_v(1-z)$} over a finite set $F$ of places of the field of rational numbers {inclusive of} the archimedean place is {quasi-inner} on the left of the critical line $\Re(z)= \frac 12$ in the following sense. The off diagonal part $u_{21}$ of the matrix of the multiplication by $u$ in the orthogonal decomposition of the Hilbert space $L^2$ of square integrable functions on the critical line into the Hardy space $H^2$ and its orthogonal complement is a compact operator. When interpreted on the unit disk, the quasi-inner condition means that the associated Haenkel matrix is compact. We show that none of the individual non-archimedean ratios $ρ_v$ is quasi-inner and, in order to prove our main result we use Gauss multiplication theorem to factor the archimedean ratio $ρ_\infty$ into a product of $m$ quasi-inner functions whose product with each $ρ_v$ retains the property to be quasi-inner. Finally we prove that Sonin's space is simply the kernel of the diagonal part $u_{22}$ for the quasi-inner function $u=ρ_\infty$, and when $u(F)=\prod_{v\in F} ρ_v$ the kernels of the $u(F)_{22}$ form an inductive system of infinite dimensional spaces which are the semi-local analogues of (classical) Sonin's spaces.
