Geodesic
Asymptotically homogeneous generalized functions and some of their applications
Informatics and Automation, Complex analysis, mathematical physics, and applications, Tome 301 (2018), pp. 74-90

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A brief description is given of generalized functions that are asymptotically homogeneous at the origin with respect to a multiplicative one-parameter transformation group such that the real parts of all eigenvalues of the infinitesimal matrix are positive. The generalized functions that are homogeneous with respect to such a group are described in full. Examples of the application of such functions in mathematical physics are given; in particular, they can be used to construct asymptotically homogeneous solutions of differential equations whose symbols are homogeneous polynomials with respect to such a group, as well as to study the singularities of holomorphic functions in tubular domains over cones.
Keywords: generalized functions, homogeneous functions, quasiasymptotics, partial differential equations. 
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     author = {Yu. N. Drozhzhinov},
     title = {Asymptotically homogeneous generalized functions and some of their applications},
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     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TRSPY_2018_301_a5/}
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Yu. N. Drozhzhinov. Asymptotically homogeneous generalized functions and some of their applications. Informatics and Automation, Complex analysis, mathematical physics, and applications, Tome 301 (2018), pp. 74-90. http://geodesic.mathdoc.fr/item/TRSPY_2018_301_a5/