We scrutinize the possibility of extending the result of [19] to the case of q-deformed oscillator for q real; for this we exploit the whole range of the deformation parameter as much as possible. We split the case into two depending on whether a solution of the commutation relation is bounded or not. Our leitmotif is subnormality. The deformation parameter q is reshaped and this is what makes our approach effective. The newly arrived parameter, the operator C, has two remarkable properties: it separates in the commutation relation the annihilation and creation operators from the deformation as well as it q-commutes with those two. This is why introducing the operator C may have far-reaching consequences.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-bc78-0-22,
author = {Franciszek Hugon Szafraniec},
title = {Operators of the q-oscillator},
journal = {Banach Center Publications},
volume = {75},
year = {2007},
pages = {293-307},
zbl = {1161.47017},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc78-0-22}
}
Franciszek Hugon Szafraniec. Operators of the q-oscillator. Banach Center Publications, Tome 75 (2007) pp. 293-307. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc78-0-22/