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

Document Type

Article

Publication Date

1-1-2001

Abstract

In this paper we will develop a systematic method to answer the questions (Q1) (Q2) (Q3) (Q4) (stated in Sec. 1) with complete generality. As a result, we can solve the difficulties (D1) (D2) (discussed in Sec. 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 {α(n)} first studied by Cochran et al.6 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 ℰc will also be discussed. * Postdoctral Fellowship at International Institute for Advanced Studies.

Publication Source (Journal or Book title)

Infinite Dimensional Analysis, Quantum Probability and Related Topics

First Page

59

Last Page

84

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