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

Ilona Królak

Banach Center Publications (1998)

  • Volume: 43, Issue: 1, page 253-257
  • ISSN: 0137-6934

Abstract

top
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 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.

How to cite

top

Królak, Ilona. "Measures connected with Bargmann's representation of the q-commutation relation for q > 1." Banach Center Publications 43.1 (1998): 253-257. <http://eudml.org/doc/208845>.

@article{Królak1998,
abstract = {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.},
author = {Królak, Ilona},
journal = {Banach Center Publications},
keywords = {moment problems; commutation relations},
language = {eng},
number = {1},
pages = {253-257},
title = {Measures connected with Bargmann's representation of the q-commutation relation for q > 1},
url = {http://eudml.org/doc/208845},
volume = {43},
year = {1998},
}

TY - JOUR
AU - Królak, Ilona
TI - Measures connected with Bargmann's representation of the q-commutation relation for q > 1
JO - Banach Center Publications
PY - 1998
VL - 43
IS - 1
SP - 253
EP - 257
AB - 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.
LA - eng
KW - moment problems; commutation relations
UR - http://eudml.org/doc/208845
ER -

References

top
  1. [1] N. Achiezer, The classical moment problem, Moscow 1959. 
  2. [2] V. Bargmann, On a Hilbert space of analytic functions and an associated integral transform, Commun. Pure and Appl. Math. XIV 187-214. Zbl0107.09102
  3. [3] M. Bożejko and R Speicher, An example of a generalized Brownian motion, Comm. Math. Phys. 137 (1991), 519-531. Zbl0722.60033
  4. [4] G. Gasper and M. Rahman, Basic hypergeometric series, Cambridge U.P., Cambridge 1990. Zbl0695.33001
  5. [5] O. W. Greenberg, Particles with small violations of Fermi or Bose statistics, Phys. Rev. D 43 (1991), 4111-4120. 
  6. [6] I. Królak, Bargmann representations and related measures, preprint. Zbl1138.81031
  7. [7] H. van Leeuven and H. Maassen, A q-deformation of the Gauss distribution, J. Math. Phys. 36(9), 4743-4756. Zbl0841.60089
  8. [8] H. van Leeuven, On q-deformed Probability Theory, Ph.D. Thesis at University of Nijmegen 1996. 
  9. [9] D. Moak, The q-analogue of the Laguerre polynomials, J. Math. Appl. 81 (1981), 20-46. Zbl0459.33009

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.