Exotic laplacians and associated stochastic processes
Exotic laplacians and associated stochastic processes
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DOI：
10.1142/s0219025709003513
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发表时间：
2009-03
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影响因子：
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通讯作者：
L. Accardi;U. Ji;Kimiaki Saitô
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文献类型：
--
作者：
L. Accardi;U. Ji;Kimiaki Saitô
本文给出了调和分布空间的塞萨罗范数分解，并对任意的奇异迹直接构造了无穷维可分Hilbert空间Hc，2a-1，其中奇异迹起着通常迹的作用.这意味着奇异拉普拉斯算子与希尔伯特空间Hc，2a-1上玻色-福克空间Γ（Hc，2a-1）中的Volterra-Gross拉普拉斯算子重合。最后我们构造了与2a-1阶奇异拉普拉斯算子自然相关的布朗运动，并得到了相关热半群的显式表达式。
In this paper, we give a decomposition of the space of tempered distributions by the Cesaro norm, and for any we construct directly from the exotic trace an infinite dimensional separable Hilbert space Hc,2a-1 on which the exotic trace plays the role as the usual trace. This implies that the Exotic Laplacian coincides with the Volterra–Gross Laplacian in the Boson Fock space Γ(Hc,2a-1) over the Hilbert space Hc,2a-1. Finally we construct the Brownian motion naturally associated to the Exotic Laplacian of order 2a-1 and we find an explicit expression for the associated heat semigroup.