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Teoriya Veroyatnostei i ee Primeneniya, 1976, Volume 21, Issue 3, Pages 640–644
(Mi tvp3409)
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Short Communications
On the orthogonality of the white noise, given on a ring of operators, relatively to multiplicative shifts
G. P. Bucan Kiev
Abstract:
The article deals with a generalized Gaussian measure on the ring of all Hilbert–Shmidt operators $G_H$ on some separable Hilbert space $H$ with the characteristic functional
$$
\varphi(z)=\exp\biggl\{-\frac{1}{2}\langle z,z\rangle\biggr\},\ \text{where}\ \forall u,v\in G_H\colon\langle u,v\rangle=\operatorname{Sp}uv^*.
$$
Conditions are studied for $\mu\sim\mu u^{-1}$ where $u\in X_H$, the set of all linear operators on $H$, and $\mu u^{-1}(F)=\mu(u^{-1}F)=\mu(v\colon uv\in F)$ for those Borel sets $F$ on $G_H$ for which this equality makes sense.
Received: 30.11.1973
Citation:
G. P. Bucan, “On the orthogonality of the white noise, given on a ring of operators, relatively to multiplicative shifts”, Teor. Veroyatnost. i Primenen., 21:3 (1976), 640–644; Theory Probab. Appl., 21:3 (1977), 624–628
Linking options:
https://www.mathnet.ru/eng/tvp3409 https://www.mathnet.ru/eng/tvp/v21/i3/p640
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Abstract page: | 143 | Full-text PDF : | 65 |
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