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

Banach Center Publications (1998)

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

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topKrólak, 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

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- [4] G. Gasper and M. Rahman, Basic hypergeometric series, Cambridge U.P., Cambridge 1990. Zbl0695.33001
- [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. Zbl1138.81031
- [7] H. van Leeuven and H. Maassen, A q-deformation of the Gauss distribution, J. Math. Phys. 36(9), 4743-4756. Zbl0841.60089
- [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. Zbl0459.33009

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