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

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

2001-04-12

arxiv.org/abs/math/0104132v1

Infinite Dimensional Analysis, Quantum Probability and Related Topics, Vol. 4, No. 1 (2001) 59-84

Mathematics

Functional Analysis

To appear in Infinite Dimensional Analysis, Quantum Probability and Related Topics 4 (2001). Universidade da Madeira CCM prepr

Scientific paper

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.

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