2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/61290In 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.To appear in Infinite Dimensional Analysis, Quantum Probability and Related Topics 4 (2001). Universidade da Madeira CCM preprint 37 (1999)Functional AnalysisProbability60H40text