Geodesic
Distributions asymptotically homogeneous along the trajectories determined by one-parameter groups
Izvestiya. Mathematics , Tome 76 (2012) no. 3, pp. 466-516.

Voir la notice de l'article provenant de la source Math-Net.Ru

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: quasi-asymptotics, Tauberian theorems, homogeneous distributions, asymptotically homogeneous functions.
Mots-clés : distributions 
@article{IM2_2012_76_3_a2,
     author = {Yu. N. Drozhzhinov and B. I. Zavialov},
     title = {Distributions asymptotically homogeneous along the trajectories determined by one-parameter groups},
     journal = {Izvestiya. Mathematics },
     pages = {466--516},
     publisher = {mathdoc},
     volume = {76},
     number = {3},
     year = {2012},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_2012_76_3_a2/}
}
TY  - JOUR
AU  - Yu. N. Drozhzhinov
AU  - B. I. Zavialov
TI  - Distributions asymptotically homogeneous along the trajectories determined by one-parameter groups
JO  - Izvestiya. Mathematics 
PY  - 2012
SP  - 466
EP  - 516
VL  - 76
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IM2_2012_76_3_a2/
LA  - en
ID  - IM2_2012_76_3_a2
ER  - 
%0 Journal Article
%A Yu. N. Drozhzhinov
%A B. I. Zavialov
%T Distributions asymptotically homogeneous along the trajectories determined by one-parameter groups
%J Izvestiya. Mathematics 
%D 2012
%P 466-516
%V 76
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IM2_2012_76_3_a2/
%G en
%F IM2_2012_76_3_a2
Yu. N. Drozhzhinov; B. I. Zavialov. Distributions asymptotically homogeneous along the trajectories determined by one-parameter groups. Izvestiya. Mathematics , Tome 76 (2012) no. 3, pp. 466-516. http://geodesic.mathdoc.fr/item/IM2_2012_76_3_a2/

[1] Yu. N. Drozhzhinov, B. I. Zav'yalov, “Generalized functions asymptotically homogeneous along special transformation groups”, Sb. Math., 200:6 (2009), 803–844 | DOI | MR | Zbl

[2] Yu. N. Drozhzhinov, B. I. Zav'yalov, “Asymptotically homogeneous generalized functions at zero and convolution equations with kernels quasi-homogeneous polynomial symbols”, Dokl. Math., 79:3 (2009), 356–359 | DOI | MR | Zbl

[3] Yu. N. Drozhzhinov, B. I. Zav'yalov, “Asymptotically quasi-homogeneous distributions”, Dokl. Math., 78:1 (2008), 503–507 | DOI | MR | Zbl

[4] 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

[5] 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

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

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

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

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

[10] I. M. Gelfand, G. E. Schilow, Verallgemeinerte Funktionen (Distributionen). I: Verallgemeinerte Funktionen und das Rechnen mit ihnen, VEB, Berlin, 1960 | MR | MR | Zbl | Zbl