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Mat. Sb., 2009, Volume 200, Number 6, Pages 23–66 (Mi msb5656)  

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.
Author to whom correspondence should be addressed

DOI: https://doi.org/10.4213/sm5656

Full text: PDF file (764 kB)
References: PDF file   HTML file

English version:
Sbornik: Mathematics, 2009, 200:6, 803–844

Bibliographic databases:

UDC: 517.5
MSC: 46F05, 46F20
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

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Yu. N. Drozhzhinov, B. I. Zavyalov, “Asimptoticheski kvaziodnorodnye obobschennye funktsii v nachale koordinat”, Ufimsk. matem. zhurn., 1:4 (2009), 24–57  mathnet  zmath
    2. Drozhzhinov Yu.N., Zav'yalov B.I., “Asymptotically homogeneous generalized functions along trajectories defined by a general one-parameter transformation group”, Dokl. Math., 82:3 (2010), 874–877  crossref  mathscinet  mathscinet  zmath  isi  elib  elib  scopus
    3. Yu. N. Drozhzhinov, B. I. Zavyalov, “Obobschennye funktsii, asimptoticheski odnorodnye vdol traektorii neustoichivogo vyrozhdennogo uzla”, Vestn. Sam. gos. tekhn. un-ta. Ser. Fiz.-mat. nauki, 1(22) (2011), 68–82  mathnet  crossref
    4. Yu. N. Drozhzhinov, B. I. Zavialov, “Homogeneous generalized functions with respect to one-parametric group”, P-Adic Num Ultrametr Anal Appl, 4:1 (2012), 64  crossref  mathscinet  zmath  scopus
    5. Yu. N. Drozhzhinov, B. I. Zavialov, “Distributions asymptotically homogeneous along the trajectories determined by one-parameter groups”, Izv. Math., 76:3 (2012), 466–516  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    6. 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  mathscinet  zmath  isi  elib  scopus
    7. 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
    8. 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
  • Математический сборник Sbornik: Mathematics (from 1967)
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