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 Izv. RAN. Ser. Mat., 2012, Volume 76, Issue 3, Pages 39–92 (Mi izv6753)

Distributions asymptotically homogeneous along the trajectories determined by one-parameter groups

Yu. N. Drozhzhinov, B. I. Zavialov

Steklov Mathematical Institute, Russian Academy of Sciences

Abstract: We give a complete description of distributions that are asymptotically homogeneous (including the case of critical index of the asymptotic scale) along the trajectories determined by continuous multiplicative one-parameter transformation groups such that the real parts of all eigenvalues of the infinitesimal matrix are positive. To do this, we introduce and study special spaces of distributions. As an application of our results, we describe distributions that are homogeneous along such groups.

Keywords: distributions, quasi-asymptotics, Tauberian theorems, homogeneous distributions, asymptotically homogeneous functions.

 Funding Agency Grant Number Russian Foundation for Basic Research 10-01-00178 Ministry of Education and Science of the Russian Federation ÍØ-2928.2012.1

DOI: https://doi.org/10.4213/im6753

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English version:
Izvestiya: Mathematics, 2012, 76:3, 466–516

Bibliographic databases:

Document Type: Article
UDC: 517.53
MSC: Primary 46F12; Secondary 44A10, 40E05
Revised: 29.04.2011

Citation: Yu. N. Drozhzhinov, B. I. Zavialov, “Distributions asymptotically homogeneous along the trajectories determined by one-parameter groups”, Izv. RAN. Ser. Mat., 76:3 (2012), 39–92; Izv. Math., 76:3 (2012), 466–516

Citation in format AMSBIB
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• http://mi.mathnet.ru/eng/izv6753
• https://doi.org/10.4213/im6753
• http://mi.mathnet.ru/eng/izv/v76/i3/p39

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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. Yu. N. Drozhzhinov, B. I. Zavialov, “Generalized functions asymptotically homogeneous with respect to one–parametric group at origin”, Ufa Math. J., 5:1 (2013), 17–35
2. Drozhzhinov Yu.N., Zav'yalov B.I., “Asymptotically Homogeneous Solutions of Differential Equations Whose Symbols Are Polynomials Quasi-Homogeneous with Respect to One-Parameter Groups with Generators Containing a Nilpotent Component”, Dokl. Math., 88:2 (2013), 590–592
3. Yu. N. Drozhzhinov, B. I. Zavialov, “Asymptotically homogeneous solutions to differential equations with homogeneous polynomial symbols with respect to a multiplicative one-parameter group”, Proc. Steklov Inst. Math., 285 (2014), 99–119
4. Yu. N. Drozhzhinov, B. I. Zavialov, “Comparison Tauberian theorems and hyperbolic operators with constant coefficients”, Ufa Math. J., 7:3 (2015), 47–53
5. Yu. N. Drozhzhinov, “Asymptotically homogeneous generalized functions and some of their applications”, Proc. Steklov Inst. Math., 301 (2018), 65–81
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