Bargmann representation of q-commutation relations for q > 1 and associated measures
Ilona Królak
Banach Center Publications, Tome 75 (2007), p. 171-183 / Harvested from The Polish Digital Mathematics Library
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The classical Bargmann representation is given by operators acting on the space of holomorphic functions with the scalar product ⟨zⁿ|zk⟩q=δn,k[n]q!=F(zⁿz̅k). 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.

Publié le : 2007-01-01
EUDML-ID : urn:eudml:doc:281985 
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     author = {Ilona Kr\'olak},
     title = {Bargmann representation of q-commutation relations for q > 1 and associated measures},
     journal = {Banach Center Publications},
     volume = {75},
     year = {2007},
     pages = {171-183},
     zbl = {1138.81031},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc78-0-13}
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Ilona Królak. Bargmann representation of q-commutation relations for q > 1 and associated measures. Banach Center Publications, Tome 75 (2007) pp. 171-183. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc78-0-13/