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

Ilona 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 -