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, M.a. (2004). Discrete q-derivatives and symmetries of q-difference equations. JOURNAL OF PHYSICS. A, MATHEMATICAL AND GENERAL, 37(10), 3459-3473 [10.1088/0305-4470/37/10/010].
Discrete q-derivatives and symmetries of q-difference equations
LEVI, Decio;
2004-01-01
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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.