The quasiasymptotic expansion at zero and generalized Watson lemma for Colombeau generalized functions

Abstract

Quasiasymptotic expansion at zero in the Colombeau algebra of generalized functions and its coherence with this notion for Schwartz distributions is given. A version of the Watson lemma related to the expansion of the Laplace transformation of an appropriate generalized Colombeau function is proved. In particular, the asymptotic expansion of δ 2 and the expansion of its Laplace transformation is given.