Publications de l'Institut Mathématique, Nouvelle Série Vol. 95[109], pp. 1–28 (2014) 

MULTIDIMENSIONAL TAUBERIAN THEOREMS FOR VECTORVALUED DISTRIBUTIONSStevan Pilipovic, Jasson VindasDepartment of Mathematics and Informatics, University of Novi Sad, Novi Sad, Serbia; Department of Mathematics, Ghent University, Gent, BelgiumAbstract: We prove several Tauberian theorems for regularizing transforms of vectorvalued distributions. The regularizing transform of $f$ is given by the integral transform $M^f_{\varphi}(x,y)=(f*\varphi_y)(x)$, $(x,y)\in\mathbb{R}^n\times\mathbb{R}_+$, with kernel $\varphi_{y}(t)=y^{n}\varphi(t/y)$. We apply our results to the analysis of asymptotic stability for a class of Cauchy problems, Tauberian theorems for the Laplace transform, the comparison of quasiasymptotics in distribution spaces, and we give a necessary and sufficient condition for the existence of the trace of a distribution on $\{x_0\}\times\mathbb R^m$. In addition, we present a new proof of Littlewood's Tauberian theorem. Keywords: Abelian and Tauberian theorems, vectorvalued distributions, quasiasymptotics, slowly varying functions, Laplace transform, wavelet transform, regularizing transforms, asymptotic behavior of generalized functions Classification (MSC2000): 40E05, 41A27; 26A12, 40E10, 41A60, 42C40, 46F10, 46F12 Full text of the article: (for faster download, first choose a mirror)
Electronic fulltext finalized on: 31 Mar 2014. This page was last modified: 2 Apr 2014.
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