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

This article is cited in 5 scientific papers (total in 5 papers)

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 НШ-2928.2012.1


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

Full text: PDF file (812 kB)
References: PDF file   HTML file

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

Bibliographic databases:

UDC: 517.53
MSC: Primary 46F12; Secondary 44A10, 40E05
Received: 10.01.2011
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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    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  mathnet  crossref  mathscinet  elib
    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  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  scopus
    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  mathnet  crossref  crossref  isi  elib  elib
    4. Yu. N. Drozhzhinov, B. I. Zavialov, “Comparison Tauberian theorems and hyperbolic operators with constant coefficients”, Ufa Math. J., 7:3 (2015), 47–53  mathnet  crossref  mathscinet  isi  elib
    5. Yu. N. Drozhzhinov, “Asymptotically homogeneous generalized functions and some of their applications”, Proc. Steklov Inst. Math., 301 (2018), 65–81  mathnet  crossref  crossref  isi  elib  elib
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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