Roles of Log-concavity, Log-convexity, and Growth Order in White Noise Analysis
نویسنده
چکیده
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 {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.
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تاریخ انتشار 2001