In this paper we extend the umbral calculus, developed to deal with difference equations on uniform lattices, to q-difference equations. We show that many properties considered for shift invariant difference operators satisfying the umbral calculus can be implemented to the case of the q-difference operators. This q-umbral calculus can be used to provide solutions to linear q-difference equations and q-differential delay equations. To illustrate the method, we will apply the obtained results to the construction of symmetry solutions for the q-heat equation.
Levi D, Negro J, & del Olmo MA (2004). Discrete q-derivatives and symmetries of q-difference equations. JOURNAL OF PHYSICS. A, MATHEMATICAL AND GENERAL, 37(10), 3459-3473.
Titolo: | Discrete q-derivatives and symmetries of q-difference equations |
Autori: | |
Data di pubblicazione: | 2004 |
Rivista: | |
Citazione: | Levi D, Negro J, & del Olmo MA (2004). Discrete q-derivatives and symmetries of q-difference equations. JOURNAL OF PHYSICS. A, MATHEMATICAL AND GENERAL, 37(10), 3459-3473. |
Abstract: | In this paper we extend the umbral calculus, developed to deal with difference equations on uniform lattices, to q-difference equations. We show that many properties considered for shift invariant difference operators satisfying the umbral calculus can be implemented to the case of the q-difference operators. This q-umbral calculus can be used to provide solutions to linear q-difference equations and q-differential delay equations. To illustrate the method, we will apply the obtained results to the construction of symmetry solutions for the q-heat equation. |
Handle: | http://hdl.handle.net/11590/136946 |
Appare nelle tipologie: | 1.1 Articolo in rivista |