Analytic version of test functionals, Fourier transform, and a characterization of measures in white noise calculus
Analytic version of test functionals, Fourier transform, and a characterization of measures in white noise calculus
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测试泛函的解析版本、傅立叶变换以及白噪声微积分测量的表征
DOI：
10.1016/0022-1236(91)90115-l
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发表时间：
1991
影响因子：
1.7
通讯作者：
Yuh
中科院分区：
文献类型：
--
作者：
Yuh
结果表明,测试白噪声的空间(J)泛函,有分析版本∞是一个代数以及拓扑线性空间拓扑化的射影限制序列{p: pϵN}的巴拿赫空间与各自的规范∥ƒ∥p =一口ZϵCJ−p{|ƒ(Z) | exp(−2−1∥Z∥)p 2]},在SJ−p表示J−p的复杂性。此外,它表明∞拓扑和(J)拓扑是等价的。在证明过程中，还证明了空间（J p）在s变换下与bJ−p上的巴格曼-西格尔解析函数是等距同构的。利用这个新版本，我们能够将广义白噪声泛函的傅里叶变换定义为参数为（1,- i）的傅里叶-维纳变换t1， - i的伴随，而且我们证明了(J)∗中的每个测度总是满足一定的“生长条件”。
It is shown that the space (J) of test white noise functionals has an analytic version A∞ which is an algebra as well as a topological linear space topologized by the projective limit of a sequence {A p: pϵ N} of Banach spaces with respective norm given by∥ ƒ∥ A p= sup Zϵ CJ− p {| ƒ (z)| exp [− 2− 1∥ z∥] p 2]}, where SJ− p denotes the complexification of J− p. Furthermore, it is shown that the A∞-topology and the (J)-topology are equivalent. In the course of the proof, it is also shown that the space (J p) is isometrically isomorphic to the Bargmann-Segal analytic functions on bJ− p under S-transform. Employing this new version, we are able to define the Fourier transform of a generalized white noise functional as the adjoint of Fourier-Wiener transform T 1,− i with parameter (1,− i), and, moreover, we show that every measure in (J)∗ always satisfies a certain “growth condition.”