标题： CKS空间关于增长函数 显示英文标题

标题： CKS-space in terms of growth functions

摘要： 引入一类增长函数$u$来构造Hida分布和测试函数。 $u$的Legendre变换$\ell_{u}$用于定义一个正数序列$\a(n)=(\ell_{u}(n) n!)^{-1}, n\geq 0$。 从这个序列我们得到一个CKS空间。 在$u$的各种条件下，我们证明相关的序列$\{\a(n)\}$满足在CKS空间上进行白噪声分布理论所需的条件。 我们证明了$u$和其对偶勒让德变换$u^{*}$分别是特征定理中测试函数和广义函数的增长函数。 显示英文摘要

摘要： A class of growth functions $u$ is introduced to construct Hida distributions and test functions. The Legendre transform $\ell_{u}$ of $u$ is used to define a sequence $\a(n)=(\ell_{u}(n) n!)^{-1}, n\geq 0$, of positive numbers. From this sequence we get a CKS-space. Under various conditions on $u$ we show that the associated sequence $\{\a(n)\}$ satisfies those conditions for carrying out the white noise distribution theory on the CKS-space. We show that $u$ and its dual Legendre transform $u^{*}$ are growth functions for test and generalized functions, respectively, in the characterization theorems.