More on deformed oscillator algebras and extended umbral calculus

Kwaśniewski, A. K., and Grądzka, E.. "More on deformed oscillator algebras and extended umbral calculus." Proceedings of the 22nd Winter School "Geometry and Physics". Palermo: Circolo Matematico di Palermo, 2003. [143]-150. <http://eudml.org/doc/220301>.

@inProceedings{Kwaśniewski2003,
abstract = {This paper deals with $\varphi (q)$ calculus which is an extension of finite operator calculus due to Rota, and leading results of Rota’s calculus are easily $\varphi $-extendable. The particular case $\varphi _n(q)= [n_\{q^1\}]^\{-1\}$ is known to be relevant for quantum group investigations. It is shown here that such $\varphi (q)$ umbral calculus leads to infinitely many new $\varphi $-deformed quantum like oscillator algebra representations. The authors point to several references dealing with new applications of $q$ umbral and $\varphi (q)$ calculus in which new families of $\varphi (q)$ extensions of Poisson processes and $q$-Bernoulli-Taylor formula with the rest $q$-term of Cauchy type are derived besides other results.},
author = {Kwaśniewski, A. K., Grądzka, E.},
booktitle = {Proceedings of the 22nd Winter School "Geometry and Physics"},
keywords = {Winter school; Geometry; Physics; Srní (Czech Republic)},
location = {Palermo},
pages = {[143]-150},
publisher = {Circolo Matematico di Palermo},
title = {More on deformed oscillator algebras and extended umbral calculus},
url = {http://eudml.org/doc/220301},
year = {2003},
}

TY - CLSWK
AU - Kwaśniewski, A. K.
AU - Grądzka, E.
TI - More on deformed oscillator algebras and extended umbral calculus
T2 - Proceedings of the 22nd Winter School "Geometry and Physics"
PY - 2003
CY - Palermo
PB - Circolo Matematico di Palermo
SP - [143]
EP - 150
AB - This paper deals with $\varphi (q)$ calculus which is an extension of finite operator calculus due to Rota, and leading results of Rota’s calculus are easily $\varphi $-extendable. The particular case $\varphi _n(q)= [n_{q^1}]^{-1}$ is known to be relevant for quantum group investigations. It is shown here that such $\varphi (q)$ umbral calculus leads to infinitely many new $\varphi $-deformed quantum like oscillator algebra representations. The authors point to several references dealing with new applications of $q$ umbral and $\varphi (q)$ calculus in which new families of $\varphi (q)$ extensions of Poisson processes and $q$-Bernoulli-Taylor formula with the rest $q$-term of Cauchy type are derived besides other results.
KW - Winter school; Geometry; Physics; Srní (Czech Republic)
UR - http://eudml.org/doc/220301
ER -