CKS-space in terms of growth functions

Details CKS-space in terms of growth functions CKS-space in terms of growth functions

2001-04-13

arxiv.org/abs/math/0104146v1

Quantum information II, T.Hida and K. Saito (eds.), World Scientific (2000) pp17--27

Mathematics

Functional Analysis

Louisiana state university preprint 1999

Scientific paper

A class of growth functions $u$ is introduced to construct Hida distributions and test functions. The Legendre transform $\ell_{u}$ of $u$ is used to define a sequence $\a(n)=(\ell_{u}(n) n!)^{-1}, n\geq 0$, of positive numbers. From this sequence we get a CKS-space. Under various conditions on $u$ we show that the associated sequence $\{\a(n)\}$ satisfies those conditions for carrying out the white noise distribution theory on the CKS-space. We show that $u$ and its dual Legendre transform $u^{*}$ are growth functions for test and generalized functions, respectively, in the characterization theorems.

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