I. Kubo

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math.FA2001

CKS-space in terms of growth functions

Nobuhiro Asai, Izumi Kubo, Hui-Hsiung Kuo

A class of growth functions $u$ is introduced to construct Hida distributions and test functions. The Legendre transform $ℓ_{u}$ of $u$ is used to define a sequence $\a(n)=(\ell…

math.FA2001

Characterization of Hida Measures in white noise analysis

Nobuhiro Asai, Izumi Kubo, Hui-Hsiung Kuo

The main purpose of this work is to prove Theorem 4.4, so-called, the characterization theorem of Hida measures (generalized measures). As examples of such measures, we shall prese…

math.FA2001

Characterization of test functions in CKS-space

Nobuhiro Asai, Izumi Kubo, Hui-Hsiung Kuo

We prove a characterization theorem for the test functions in a CKS-space. Some crucial ideas concerning the growth condition are given.

math.FA2001

General characterization theorems and intrinsic topologies in white noise analysis

Nobuhiro Asai, Izumi Kubo, Hui-Hsiung Kuo

Let $u$ be a positive continuous function on $[0, \infty)$ satisfying the conditions: (i) $lim_{r \to \infty} r^{- 1/2} lo g u (r) = \infty$ , (ii) $in f_{r \geq 0} u (r) = 1$ , (iii) $\lim_{r…

math.FA2001

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

Nobuhiro Asai, Izumi Kubo, Hui-Hsiung Kuo

In this paper we will develop a systematic method to answer the questions $(Q 1) (Q 2) (Q 3) (Q 4)$ (stated in Section 1) with complete generality. As a result, we can solve the difficult…