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