Existence and Uniqueness of v-Asymptotic Expansions and Colombeau’s Generalized Numbers
نویسنده
چکیده
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. Mathematics Subject Classification: 30B10, 34E05, 35D05, 41A60, 40A30, 46F30.
منابع مشابه
Existence and uniqueness of v-asymptotic expansions and Colombeauâ•Žs generalized numbers
We define a type of generalized asymptotic series called v-asymptotic. We show that every func tion 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 ex pansion. As an application to random matrix theory we calculate the coefficients and establish the uniqueness ...
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