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Sbornik: Mathematics, 2009, Volume 200, Issue 6, Pages 803–844
DOI: https://doi.org/10.1070/SM2009v200n06ABEH004020 (Mi sm5656) 		 
This article is cited in 8 scientific papers (total in 8 papers)

Generalized functions asymptotically homogeneous along special transformation groups

Yu. N. Drozhzhinov, B. I. Zavialov

Steklov Mathematical Institute, Russian Academy of Sciences
English version PDF (494 kB) Citations (8)
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DOI: https://doi.org/10.1070/SM2009v200n06ABEH004020
Abstract: Distributions having (quasi)asymptotics in the asymptotic scale of regularly varying functions along special groups of transformation of independent variables are said to be asymptotically homogeneous along these transformation groups. In particular, all ‘quasihomogeneous’ distributions have this property. A complete description of asymptotically homogeneous distributions along a transformation group determined by a vector $a\in\mathbb R_+^n$ is obtained, including in the case of critical orders. Special distribution spaces are introduced and investigated to this end. The results obtained are used for the analysis of singularities of holomorphic functions in the tube domains over coordinate sectors.
Bibliography: 10 titles.
Keywords: distributions, Tauberian theorems, holomorphic functions.
Received: 17.04.2008 and 27.11.2008
Russian version:
Matematicheskii Sbornik, 2009, Volume 200, Number 6, Pages 23–66
DOI: https://doi.org/10.4213/sm5656
Bibliographic databases:
Document Type: Article
UDC: 517.5
MSC: 46F05, 46F20
Language: English
Original paper language: Russian
Citation: Yu. N. Drozhzhinov, B. I. Zavialov, “Generalized functions asymptotically homogeneous along special transformation groups”, Mat. Sb., 200:6 (2009), 23–66; Sb. Math., 200:6 (2009), 803–844
Citation in format AMSBIB
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    • This publication is cited in the following 8 articles:
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