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Structural theorems for quasiasymptotics of distributions at the origin
Author(s) -
Vindas Jasson,
Pilipović S.
Publication year - 2009
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.200710090
Subject(s) - converse , mathematics , homogeneous , distribution (mathematics) , pure mathematics , mathematical analysis , combinatorics , geometry
An open question concerning the quasiasymptotic behavior of distributions at the origin is solved. The question is the following: Suppose that a tempered distribution has quasiasymptotic at the origin in S ′(ℝ), then the tempered distribution has quasiasymptotic in D ′(ℝ), does the converse implication hold? The second purpose of this article is to give complete structural theorems for quasiasymptotics at the origin. For this purpose, asymptotically homogeneous functions with respect to slowly varying functions are introduced and analyzed (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)