More on deformed oscillator algebras and extended umbral calculus

Proceedings of the 22nd Winter School "Geometry and Physics", GDML_Books, (2003), p. [143]-150 / Harvested from

Résumé

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 $ϕ_{n} (q) = {[n_{q^{1}}]}^{- 1}$ 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.

MR MR1982441 | Zbl 1031.05018

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/