Pełnotekstowe zasoby PLDML oraz innych baz dziedzinowych są już dostępne w nowej Bibliotece Nauki.
Zapraszamy na https://bibliotekanauki.pl

PL EN


Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
1998 | 43 | 1 | 253-257

Tytuł artykułu

Measures connected with Bargmann's representation of the q-commutation relation for q > 1

Autorzy

Treść / Zawartość

Języki publikacji

EN

Abstrakty

EN
Classical Bargmann's representation is given by operators acting on the space of holomorphic functions with scalar product $〈z^n,z^k〉_q = δ_{n,k}[n]_q! = F(z^n \bar{z}^k)$. We consider the problem of representing the functional F as a measure. We prove the existence of such a measure for q > 1 and investigate some of its properties like uniqueness and radiality.

Rocznik

Tom

43

Numer

1

Strony

253-257

Daty

wydano
1998

Twórcy

  • Institute of Mathematics, Wrocław University, pl. Grunwaldzki 2/4, 50-384 Wrocław, Poland

Bibliografia

  • [1] N. Achiezer, The classical moment problem, Moscow 1959.
  • [2] V. Bargmann, On a Hilbert space of analytic functions and an associated integral transform, Commun. Pure and Appl. Math. XIV 187-214.
  • [3] M. Bożejko and R Speicher, An example of a generalized Brownian motion, Comm. Math. Phys. 137 (1991), 519-531.
  • [4] G. Gasper and M. Rahman, Basic hypergeometric series, Cambridge U.P., Cambridge 1990.
  • [5] O. W. Greenberg, Particles with small violations of Fermi or Bose statistics, Phys. Rev. D 43 (1991), 4111-4120.
  • [6] I. Królak, Bargmann representations and related measures, preprint.
  • [7] H. van Leeuven and H. Maassen, A q-deformation of the Gauss distribution, J. Math. Phys. 36(9), 4743-4756.
  • [8] H. van Leeuven, On q-deformed Probability Theory, Ph.D. Thesis at University of Nijmegen 1996.
  • [9] D. Moak, The q-analogue of the Laguerre polynomials, J. Math. Appl. 81 (1981), 20-46.

Identyfikator YADDA

bwmeta1.element.bwnjournal-article-bcpv43i1p253bwm