EMIS ELibM Electronic Journals Publications de l'Institut Mathématique, Nouvelle Série
Vol. 84(98), pp. 159–174 (2008)

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STRUCTURAL THEOREMS FOR QUASIASYMPTOTICS OF DISTRIBUTIONS AT INFINITY

Jasson Vindas

Department of Mathematics, Louisiana State University

Abstract: Complete structural theorems for quasiasymptotics of distributions are presented in this article. For this, asymptotically homogeneous functions and associate asymptotically homogeneous functions at infinity with respect to a slowly varying function are employed. The proposed analysis, based on the concept of asymptotically and associate asymptotically homogeneous functions, allows to obtain easier proofs of the structural theorems for quasiasymptotics at infinity in the so far only known case: when the degree of the quasiasymptotic is not a negative integer. Furthermore, new structural theorems for the case of negative integral degrees are obtained by this method.

Keywords: Slowly varying functions, quasiasymptotics of distributions, almost homogeneous functions

Classification (MSC2000): 41A60, 46F10; 42A24, 46F05, 46F99

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Electronic fulltext finalized on: 9 Dec 2008. This page was last modified: 12 Dec 2008.

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© 2008 ELibM and FIZ Karlsruhe / Zentralblatt MATH for the EMIS Electronic Edition