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

Nobuhiro Asai; Izumi Kubo; Hui-Hsiung Kuo

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

Functional Analysis 2007-05-23 v1 Probability

Authors: Nobuhiro Asai , Izumi Kubo , Hui-Hsiung Kuo

Abstract

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.

Keywords

log-concavity log-convexity growth order white noise analysis Legendre transform growth functions weight sequence

Cite

@article{arxiv.math/0104132,
  title  = {Roles of Log-concavity, log-convexity, and growth order in white noise analysis},
  author = {Nobuhiro Asai and Izumi Kubo and Hui-Hsiung Kuo},
  journal= {arXiv preprint arXiv:math/0104132},
  year   = {2007}
}

Comments

To appear in Infinite Dimensional Analysis, Quantum Probability and Related Topics 4 (2001). Universidade da Madeira CCM preprint 37 (1999)

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

Abstract

Keywords

Cite

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