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Języki publikacji
Abstrakty
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.
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Czasopismo
Rocznik
Tom
Numer
Strony
253-257
Opis fizyczny
Daty
wydano
1998
Twórcy
autor
- 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.
Typ dokumentu
Bibliografia
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