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.
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].
File in questo prodotto:
Non ci sono file associati a questo prodotto.

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11590/136946
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 15
  • ???jsp.display-item.citation.isi??? 16
social impact