Itogi Nauki i Tekhniki. Seriya "Sovremennye Problemy Matematiki. Noveishie Dostizheniya"
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Itogi Nauki i Tekhniki. Ser. Sovrem. Probl. Mat. Nov. Dostizh.:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Itogi Nauki i Tekhniki. Seriya "Sovremennye Problemy Matematiki. Noveishie Dostizheniya", 1989, Volume 36, Pages 103–147 (Mi intd122)  

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.
English version:
Journal of Soviet Mathematics, 1991, Volume 56, Issue 5, Pages 2670–2697
DOI: https://doi.org/10.1007/BF01095976
Bibliographic databases:
Document Type: Article
UDC: 519.248.3
Language: Russian
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
Citation in format AMSBIB
\Bibitem{Hol89}
\by A.~S.~Holevo
\paper Conditionally positive-definite functions in quantum probability theory
\serial Itogi Nauki i Tekhniki. Ser. Sovrem. Probl. Mat. Nov. Dostizh.
\yr 1989
\vol 36
\pages 103--147
\publ VINITI
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/intd122}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1057198}
\zmath{https://zbmath.org/?q=an:0735.46044}
\transl
\jour J. Soviet Math.
\yr 1991
\vol 56
\issue 5
\pages 2670--2697
\crossref{https://doi.org/10.1007/BF01095976}
Linking options:
  • https://www.mathnet.ru/eng/intd122
  • https://www.mathnet.ru/eng/intd/v36/p103
  • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Statistics & downloads:
    Abstract page:540
    Full-text PDF :186
     
      Contact us:
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2024