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.
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http://hdl.handle.net/11590/136946
Titolo: | Discrete q-derivatives and symmetries of q-difference equations |
Autori: | |
Data di pubblicazione: | 2004 |
Rivista: | |
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 |
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