Structural theorems for quasiasymptotics of distributions at the origin |
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| Authors: | Jasson Vindas S. Pilipović |
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| Affiliation: | 1. Mathematics Department, Louisiana State University, Baton Rouge, LA 70803, USA;2. University of Novi Sad, Department of Mathematics and Informatics, Trg Dositeja Obradovi?a 4, 21000 Novi Sad, Serbia |
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| Abstract: | 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 ′(?), then the tempered distribution has quasiasymptotic in D ′(?), 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) |
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| Keywords: | Slowly varying functions quasiasymptotics of distributions almost homogeneous functions |
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