Un théorème de dualité entre espaces de fonctions holomorphes à croissance exponentielle

Abstract

Soit %* la fonction conjugue e de % et G %* (N ) l'espace des fonctions holomorphes sur N et qui ve rifient: il existe p # N, m>0 et M 0 telle que:On de montre que la transforme e de Laplace re alise un isomorphisme topologique entre le dual fort de F % (N$) et G %* (N ). On donne ensuite des applications de ce re sultat aÁ l'analyse du bruit blanc. Academic PressLet N$ be the dual of a nuclear Fre chet space N and % a Young function on [0, + [. We define the space F % (N$) of holomorphic functions on N$ which satisfy: for all m>0 and p # N there exists K 0 such thatLet %* be the conjugate function of % and G %* (N ) the space of holomorphic functions on N which satisfy: there exists p # N, m>0 and M 0 such thatWe prove that the Laplace transform realizes a topological isomorphism of the strong dual of F %

A Quantum Approach to Laplace Operators

“…The algebraic stochastic process j = {j t ; t ≥ 0} acting on W 0 (K S ), given by (4.1), satisfies the following classical diffusion equation 15) where g = (g k ) is an arbitrary orthonormal basis of K S,r , L is the generator of the semigroup P t defined in Proposition 4.2 and…”

The q-Gamma White Noise

“…Also a space of holomorphic functions on the complexification of E α,q with θ-exponential growth which is the analogue of the Gaussian case (where θ is the Young function) can be introduced. We expect to develop a new quantum q-Gamma white noise operator theory as an analogue of the quantum white noise operator theory, (see [2]- [6], [11]- [13]). …”

Stokes formula on the space of tempered distributions

“…We will assume that the Young function θ satisfies the condition lim t→∞ θ(t) t 2 < ∞. In that case, we have a Gel'fand triple by [4]:…”