标题： 对数凸性、对数凹性和增长阶在白噪声分析中的作用 显示英文标题

标题： Roles of Log-concavity, log-convexity, and growth order in white noise analysis

摘要： 在本文中，我们将开发一种系统的方法来回答问题$(Q1)(Q2)(Q3)(Q4)$（在第1节中陈述）并具有完全的普遍性。 作为结果，我们可以解决困难$(D1)(D2)$（在第1节中讨论）而没有不确定性。 为了这些目的，我们将引入某些增长函数类$u$并应用勒让德变换以得到一个序列，该序列导致权重序列$\{\a(n)\}$，首先由Cochran等人研究。 \cite{cks}。 （几乎）等价函数、（几乎）等价序列和对偶勒让德函数的概念将以非常自然的方式定义。 还将讨论对全纯函数在$\ce_c$上的增长阶的应用。 显示英文摘要

摘要： In this paper we will develop a systematic method to answer the questions $(Q1)(Q2)(Q3)(Q4)$ (stated in Section 1) with complete generality. As a result, we can solve the difficulties $(D1)(D2)$ (discussed in Section 1) without uncertainty. For these purposes we will introduce certain classes of growth functions $u$ and apply the Legendre transform to obtain a sequence which leads to the weight sequence $\{\a(n)\}$ first studied by Cochran et al. \cite{cks}. The notion of (nearly) equivalent functions, (nearly) equivalent sequences and dual Legendre functions will be defined in a very natural way. An application to the growth order of holomorphic functions on $\ce_c$ will also be discussed.