Geodesic
Generalized functions asymptotically homogeneous along special transformation groups
Sbornik. Mathematics, Tome 200 (2009) no. 6, pp. 803-844

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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 
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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/