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The quasiasymptotic expansion at zero and generalized Watson lemma for Colombeau generalized functions. (English) Zbl 1061.41024

Quasiasymptotic expansions at zero in the Colombeau algebra of generalized functions and its coherence with this notion for Schwartz distributions is given. A version of Watson’s lemma related to the expansion of the Laplace transform of an appropriate generalized Colombeau function is proved. In particular, the asymptotic expansion of \(\delta^2\) and the expansion of its Laplace transform is given.

MSC:

41A60 Asymptotic approximations, asymptotic expansions (steepest descent, etc.)
46F30 Generalized functions for nonlinear analysis (Rosinger, Colombeau, nonstandard, etc.)
44A10 Laplace transform
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