| Title:
|
More on deformed oscillator algebras and extended umbral calculus (English) |
| Author:
|
Kwaśniewski, A. K. |
| Author:
|
Grądzka, E. |
| Language:
|
English |
| Journal:
|
Proceedings of the 22nd Winter School "Geometry and Physics" |
| Volume:
|
|
| Issue:
|
2002 |
| Year:
|
|
| Pages:
|
[143]-150 |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| MSC:
|
05A40 |
| MSC:
|
81R50 |
| idZBL:
|
Zbl 1031.05018 |
| idMR:
|
MR1982441 |
| . |
| Date available:
|
2009-07-13T21:49:24Z |
| Last updated:
|
2025-06-26 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/701713 |
| . |
