Geodesic
Generalized functions asymptotically homogeneous along special transformation groups
Sbornik. Mathematics, Tome 200 (2009) no. 6, pp. 803-844 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

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: Tauberian theorems, holomorphic functions.
Mots-clés : distributions 
@article{SM_2009_200_6_a1,
     author = {Yu. N. Drozhzhinov and B. I. Zavialov},
     title = {Generalized functions asymptotically homogeneous along special transformation groups},
     journal = {Sbornik. Mathematics},
     pages = {803--844},
     year = {2009},
     volume = {200},
     number = {6},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2009_200_6_a1/}
}
TY  - JOUR
AU  - Yu. N. Drozhzhinov
AU  - B. I. Zavialov
TI  - Generalized functions asymptotically homogeneous along special transformation groups
JO  - Sbornik. Mathematics
PY  - 2009
SP  - 803
EP  - 844
VL  - 200
IS  - 6
UR  - http://geodesic.mathdoc.fr/item/SM_2009_200_6_a1/
LA  - en
ID  - SM_2009_200_6_a1
ER  - 
%0 Journal Article
%A Yu. N. Drozhzhinov
%A B. I. Zavialov
%T Generalized functions asymptotically homogeneous along special transformation groups
%J Sbornik. Mathematics
%D 2009
%P 803-844
%V 200
%N 6
%U http://geodesic.mathdoc.fr/item/SM_2009_200_6_a1/
%G en
%F SM_2009_200_6_a1
Yu. N. Drozhzhinov; B. I. Zavialov. Generalized functions asymptotically homogeneous along special transformation groups. Sbornik. Mathematics, Tome 200 (2009) no. 6, pp. 803-844. http://geodesic.mathdoc.fr/item/SM_2009_200_6_a1/

[1] Eu. Seneta, Regularly varying functions, Lecture Notes in Math., 508, Springer-Verlag, Berlin–Heidelberg–New York, 1976 | DOI | MR | MR | Zbl | Zbl

[2] O. von Grudzinski, Quasihomogeneous distributions, North-Holland Math. Stud., 165, North-Holland, Amsterdam, 1991 | MR | Zbl

[3] Yu. N. Drozhzhinov, B. I. Zav'yalov, “Asymptotically homogeneous generalized functions in spherical representation and applications”, Dokl. Math., 72:3 (2005), 839–542 | MR | Zbl

[4] V. S. Vladimirov, Yu. N. Drozhzhinov, B. I. Zavyalov, Mnogomernye tauberovy teoremy dlya obobschennykh funktsii, Nauka, M., 1986 | MR | Zbl

[5] H. H. Schaefer, Topological vector spaces, Macmillan, New York–London, 1966 | MR | MR | Zbl | Zbl

[6] I. M. Gel'fand, G. E. Shilov, Generalized functions. Vol. I: Properties and operations, Academic Press, New York–London, 1964 | MR | MR | Zbl

[7] V. S. Vladimirov, Generalized functions in mathematical physics, Mir, Moscow, 1979 | MR | MR | Zbl | Zbl

[8] Yu. N. Drozhzhinov, B. I. Zav'yalov, “Asymptotically homogeneous generalized functions and boundary properties of functions holomorphic in tubular cones”, Izv. Math., 70:6 (2006), 1117–1164 | DOI | MR | Zbl

[9] A. N. Kolmogorov, S. V. Fomin, Elementy teorii funktsii i funktsionalnogo analiza, 4-e izd., Nauka, M., 1976 ; A. N. Kolmogorov, S. V. Fomin, Introductory real analysis, Prentice-Hall, Englewood Cliffs, NJ, 1970 | MR | Zbl | MR | Zbl

[10] V. S. Vladimirov, Methods of the theory of functions of many complex variables, Cambridge, MA–London, MIT Press, 1966 | MR | MR | Zbl