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

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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 
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     author = {Yu. N. Drozhzhinov and B. I. Zavialov},
     title = {Distributions asymptotically homogeneous along the trajectories determined by one-parameter groups},
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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/