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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
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
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
Linking options:
https://www.mathnet.ru/eng/sm5656https://doi.org/10.1070/SM2009v200n06ABEH004020 https://www.mathnet.ru/eng/sm/v200/i6/p23
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Abstract page: | 576 | Russian version PDF: | 212 | English version PDF: | 15 | References: | 84 | First page: | 4 |
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