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Izv. RAN. Ser. Mat., 2006, Volume 70, Issue 6, Pages 45–92 (Mi izv866)  

This article is cited in 11 scientific papers (total in 11 papers)

Asymptotically homogeneous generalized functions and boundary properties of functions holomorphic in tubular cones

Yu. N. Drozhzhinov, B. I. Zavialov

Steklov Mathematical Institute, Russian Academy of Sciences

Abstract: We introduce and study a spherical representation of generalized functions and use it to give a complete description of asymptotically homogeneous generalized functions in the case when the order is non-critical and sufficient conditions when it is critical. Generalized functions of slow growth (tempered distributions) that have (quasi-)asymptotics at infinity in the asymptotic scale of regularly varying functions are said to be asymptotically homogeneous. In particular, all homogeneous generalized functions are asymptotically homogeneous. We apply our results to the study of singularities of holomorphic functions in tubular domains over cones.

DOI: https://doi.org/10.4213/im866

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English version:
Izvestiya: Mathematics, 2006, 70:6, 1117–1164

Bibliographic databases:

Document Type: Article
UDC: 517.5
MSC: 46F12, 40E05, 44A15
Received: 22.02.2006

Citation: Yu. N. Drozhzhinov, B. I. Zavialov, “Asymptotically homogeneous generalized functions and boundary properties of functions holomorphic in tubular cones”, Izv. RAN. Ser. Mat., 70:6 (2006), 45–92; Izv. Math., 70:6 (2006), 1117–1164

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, “Vvedenie v teoriyu obobschennykh funktsii”, Lekts. kursy NOTs, 5, MIAN, M., 2006, 3–162  mathnet  crossref  zmath  elib
    2. Yu. N. Drozhzhinov, B. I. Zavyalov, “Asimptoticheski kvaziodnorodnye obobschennye funktsii v nachale koordinat”, Ufimsk. matem. zhurn., 1:4 (2009), 24–57  mathnet  zmath
    3. Yu. N. Drozhzhinov, B. I. Zavialov, “Generalized functions asymptotically homogeneous along special transformation groups”, Sb. Math., 200:6 (2009), 803–844  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    4. 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  zmath  isi  elib  elib  scopus
    5. 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
    6. Vindas J., “Regularizations at the origin of distributions having prescribed asymptotic properties”, Integral Transforms Spec. Funct., 22:4-5 (2011), 375–382  crossref  mathscinet  zmath  isi  elib  scopus
    7. 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
    8. 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
    9. S. Kostadinova, S. Pilipović, K. Saneva, J. Vindas, “The Ridgelet transform of distributions”, Integral Transforms and Special Functions, 2013, 1  crossref  mathscinet  isi  scopus
    10. Pilipovic S. Vindas J., “Multidimensional Tauberian Theorems For Vector-Valued Distributions”, Publ. Inst. Math.-Beograd, 95:109 (2014), 1–28  crossref  mathscinet  zmath  isi  scopus
    11. Yu. N. Drozhzhinov, “Multidimensional Tauberian theorems for generalized functions”, Russian Math. Surveys, 71:6 (2016), 1081–1134  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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