Geodesic
Conditionally positive-definite functions in quantum probability theory
Itogi Nauki i Tekhniki. Seriya Sovremennye Problemy Matematiki. Noveishie Dostizheniya, Tome 36 (1989), pp. 103-147.

Voir la notice de l'article provenant de la source Math-Net.Ru

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. 
@article{INTD_1989_36_a3,
     author = {A. S. Holevo},
     title = {Conditionally positive-definite functions in quantum probability theory},
     journal = {Itogi Nauki i Tekhniki. Seriya Sovremennye Problemy Matematiki. Noveishie Dostizheniya},
     pages = {103--147},
     publisher = {mathdoc},
     volume = {36},
     year = {1989},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTD_1989_36_a3/}
}
TY  - JOUR
AU  - A. S. Holevo
TI  - Conditionally positive-definite functions in quantum probability theory
JO  - Itogi Nauki i Tekhniki. Seriya Sovremennye Problemy Matematiki. Noveishie Dostizheniya
PY  - 1989
SP  - 103
EP  - 147
VL  - 36
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/INTD_1989_36_a3/
LA  - ru
ID  - INTD_1989_36_a3
ER  - 
%0 Journal Article
%A A. S. Holevo
%T Conditionally positive-definite functions in quantum probability theory
%J Itogi Nauki i Tekhniki. Seriya Sovremennye Problemy Matematiki. Noveishie Dostizheniya
%D 1989
%P 103-147
%V 36
%I mathdoc
%U http://geodesic.mathdoc.fr/item/INTD_1989_36_a3/
%G ru
%F INTD_1989_36_a3
A. S. Holevo. Conditionally positive-definite functions in quantum probability theory. Itogi Nauki i Tekhniki. Seriya Sovremennye Problemy Matematiki. Noveishie Dostizheniya, Tome 36 (1989), pp. 103-147. http://geodesic.mathdoc.fr/item/INTD_1989_36_a3/