More on deformed oscillator algebras and extended umbral calculus
Kwaśniewski, A. K. ; Grądzka, E.
Proceedings of the 22nd Winter School "Geometry and Physics", GDML_Books, (2003), p. [143]-150 / Harvested from

This paper deals with ϕ(q) calculus which is an extension of finite operator calculus due to Rota, and leading results of Rota’s calculus are easily ϕ-extendable. The particular case ϕn(q)=[nq1]-1 is known to be relevant for quantum group investigations. It is shown here that such ϕ(q) umbral calculus leads to infinitely many new ϕ-deformed quantum like oscillator algebra representations. The authors point to several references dealing with new applications of q umbral and ϕ(q) calculus in which new families of ϕ(q) extensions of Poisson processes and q-Bernoulli-Taylor formula with the rest q-term of Cauchy type are derived besides other results.

EUDML-ID : urn:eudml:doc:220301
Mots clés:
@article{701713,
     title = {More on deformed oscillator algebras and extended umbral calculus},
     booktitle = {Proceedings of the 22nd Winter School "Geometry and Physics"},
     series = {GDML\_Books},
     publisher = {Circolo Matematico di Palermo},
     address = {Palermo},
     year = {2003},
     pages = {[143]-150},
     mrnumber = {MR1982441},
     zbl = {1031.05018},
     url = {http://dml.mathdoc.fr/item/701713}
}
Kwaśniewski, A. K.; Grądzka, E. More on deformed oscillator algebras and extended umbral calculus, dans Proceedings of the 22nd Winter School "Geometry and Physics", GDML_Books,  (2003), pp. [143]-150. http://gdmltest.u-ga.fr/item/701713/