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- W1966643381 abstract "We define a type of generalized asymptotic series called $v$-asymptotic. We show that every function with moderate growth at infinity has a $v$-asymptotic expansion. We also describe the set of $v$-asymptotic series, where a given function with moderate growth has a unique $v$-asymptotic expansion. As an application to random matrix theory we calculate the coefficients and establish the uniqueness of the $v$-asymptotic expansion of an integral with a large parameter. As another application (with significance in the non-linear theory of generalized functions) we show that every Colombeau's generalized number has a $v$-asymptotic expansion. A similar result follows for Colombeau's generalized functions, in particular, for all Schwartz distributions." @default.
- W1966643381 created "2016-06-24" @default.
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- W1966643381 date "2005-12-01" @default.
- W1966643381 modified "2023-09-29" @default.
- W1966643381 title "Existence and uniqueness of v-asymptotic expansions and Colombeau's generalized numbers" @default.
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- W1966643381 doi "https://doi.org/10.1016/j.jmaa.2005.03.042" @default.
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