Geodesic
On the L\'evy--Khinchin formula in noncommutative probability theory
Teoriâ veroâtnostej i ee primeneniâ, Tome 38 (1993) no. 4, pp. 842-857

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An important role in modern statistical quantum measurement theory is played by measures that assume values in a noncommutative algebra of transformations. This paper investigates convolution semigroups of such measures arising in connection with measurement processes that proceed continuously in time. The principal result is a noncommutative generalization of the Lévy–Khinchin formula, which describes the structure of the convolution semigroups in terms of their Fourier transforms.
Keywords: convolution semigroup, quasi-characteristic function.
Mots-clés : instrument 
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     author = {A. S. Kholevo},
     title = {On the {L\'evy--Khinchin} formula in noncommutative probability theory},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {842--857},
     publisher = {mathdoc},
     volume = {38},
     number = {4},
     year = {1993},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1993_38_4_a7/}
}
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A. S. Kholevo. On the L\'evy--Khinchin formula in noncommutative probability theory. Teoriâ veroâtnostej i ee primeneniâ, Tome 38 (1993) no. 4, pp. 842-857. http://geodesic.mathdoc.fr/item/TVP_1993_38_4_a7/