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Itogi Nauki i Tekhniki. Seriya "Sovremennye Problemy Matematiki. Noveishie Dostizheniya", 1989, Volume 36, Pages 103–147
(Mi intd122)
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This article is cited in 2 scientific papers (total in 2 papers)
Conditionally positive-definite functions in quantum probability theory
A. S. Holevo
Abstract:
The author introduces the concepts of positive-definite and conditionally positive definite functions with values in the algebra of bounded maps of a $C^*$-algebra. An analog of Schoenberg's theorem is proved, a GNS-representation is obtained for conditionally positive-definite functions in terms of suitable cocycles, and this representation leads to a noncommutative generalization of the Lévy–Khinchin formula. Applications to the problem of continuous measurement in quantum mechanics are considered. A complete mathematical description is presented of continuous measurement processes, based on the analogy with the classical parts of probability theory — the theory of infinitely divisible distributions and functional limit theorems for processes with independent increments.
Citation:
A. S. Holevo, “Conditionally positive-definite functions in quantum probability theory”, Itogi Nauki i Tekhniki. Ser. Sovrem. Probl. Mat. Nov. Dostizh., 36, VINITI, Moscow, 1989, 103–147; J. Soviet Math., 56:5 (1991), 2670–2697
Linking options:
https://www.mathnet.ru/eng/intd122 https://www.mathnet.ru/eng/intd/v36/p103
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Abstract page: | 540 | Full-text PDF : | 186 |
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