Generalized functions asymptotically homogeneous along special transformation groups
Yurii Nikolaevich Drozhzhinov, Boris Ivanovich Zav'yalov · Sbornik Mathematics · 2009
Distributions having (quasi)asymptotics in the asymptotic scale of regularly varying functions along special groups of transforma- tion 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 2 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.