# Bargmann representation of q-commutation relations for q > 1 and associated measures

Banach Center Publications (2007)

- Volume: 78, Issue: 1, page 171-183
- ISSN: 0137-6934

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topIlona Królak. "Bargmann representation of q-commutation relations for q > 1 and associated measures." Banach Center Publications 78.1 (2007): 171-183. <http://eudml.org/doc/281985>.

@article{IlonaKrólak2007,

abstract = {The classical Bargmann representation is given by operators acting on the space of holomorphic functions with the scalar product $⟨zⁿ|z^k⟩_q = δ_\{n,k\}[n]_q! = F(zⁿz̅^k)$. We consider the problem of representing the functional F as a measure for q > 1. We prove the existence of such a measure and investigate some of its properties like uniqueness and radiality. The above problem is closely related to the indeterminate Stieltjes moment problem.},

author = {Ilona Królak},

journal = {Banach Center Publications},

keywords = {commutation relations; moment problem},

language = {eng},

number = {1},

pages = {171-183},

title = {Bargmann representation of q-commutation relations for q > 1 and associated measures},

url = {http://eudml.org/doc/281985},

volume = {78},

year = {2007},

}

TY - JOUR

AU - Ilona Królak

TI - Bargmann representation of q-commutation relations for q > 1 and associated measures

JO - Banach Center Publications

PY - 2007

VL - 78

IS - 1

SP - 171

EP - 183

AB - The classical Bargmann representation is given by operators acting on the space of holomorphic functions with the scalar product $⟨zⁿ|z^k⟩_q = δ_{n,k}[n]_q! = F(zⁿz̅^k)$. We consider the problem of representing the functional F as a measure for q > 1. We prove the existence of such a measure and investigate some of its properties like uniqueness and radiality. The above problem is closely related to the indeterminate Stieltjes moment problem.

LA - eng

KW - commutation relations; moment problem

UR - http://eudml.org/doc/281985

ER -

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