The Segal-Bargmann transform for Levy functionals
The Segal-Bargmann transform for Levy functionals
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DOI：
10.1006/jfan.1999.3452
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发表时间：
1999-10
影响因子：
1.7
通讯作者：
Yuh-Jia Lee;Hsin-Hung Shih
中科院分区：
文献类型：
--
作者：
Yuh-Jia Lee;Hsin-Hung Shih
设S′是R上的调和分布空间，Λ是S′上的Levy噪声测度.本文给出了L2（S′，Λ）上Levy泛函的Segal-Bargmann变换（或S-变换）的封闭形式，证明了S-变换是从L2（S ′，Λ）到L2（R2，λ）上Bargmann-Segal解析函数空间的酉算子，其中dλ=dt <$u2 dβ0（u），β0是Levy测度.
Let S′ be the space of tempered distributions on R and Λ the Levy noise measure on S′. In this paper, we derive the closed form of the Segal–Bargmann transform (or the S-transform) of the Levy functionals on L2(S′, Λ) and show that S-transform is a unitary operator from L2(S′, Λ) onto the space of Bargmann–Segal analytic functions on L2(R2, λ), where dλ=dt⊕u2 dβ0(u) and β0 is the Levy measure.