On the asymptotic expansion of some integrals
type: Item
instance of: scholarly article
title: On the asymptotic expansion of some integrals
zbMATH Open document ID: 0531.41027
DOI: 10.1007/BF01191183
author: Jochen Brüning
published in: Archiv der Mathematik
publication date: 1984-01-01T00:00:00Z
review text: This note deals with integrals of the form \[ I(s,f):=\int_{{\mathbb{R}}^ n}g(x^{\alpha}/s)x^{\beta}\log^{\gamma}xf(x)dx \] where \(g\in S({\mathbb{R}}^ n)\) (the Schwartz space), \(f\in C_ 0^{\infty}({\mathbb{R}}^ n)\), \(s>0\), and \(\alpha,\beta \in {\mathbb{R}}^ n\) with \(\alpha_ i>0\), \(\beta_ i\geq 0\), 1\(\leq i\leq n\), \(\gamma \in {\mathbb{Z}}^ n_+\). The asymptotic expansion of I(s,f) as \(s\to 0\) is derived by induction on n using a two-variable asymptotic expansion in the induction step. As a special case one obtains a recent result of \textit{D. Barlet} [Invent. Math. 68, 129-174 (1982; Zbl 0508.32003)].
Mathematics Subject Classification ID: 41A60
zbMATH DE Number: 3842447
zbMATH Keywords: asymptotic expansions for integrals
MaRDI profile type: Publication
cites work: Développement asymptotique des fonctions obtenues par intégration sur les fibres
cites work: The asymptotic expansion of Minakshisundaram-Pleijel in the equivariant case
cites work: Q5724171
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cites work: Intégrales asymptotiques et monodromie
description: scientific article; zbMATH DE number 3842447