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Trudy Mat. Inst. Steklova, 2018, Volume 301, Pages 74–90 (Mi tm3899)  

Asymptotically homogeneous generalized functions and some of their applications

Yu. N. Drozhzhinov

Steklov Mathematical Institute of Russian Academy of Sciences, ul. Gubkina 8, Moscow, 119991 Russia

Abstract: 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.

DOI: https://doi.org/10.1134/S0371968518020061

Full text: PDF file (252 kB)
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English version:
Proceedings of the Steklov Institute of Mathematics, 2018, 301, 65–81

Bibliographic databases:

UDC: 517.53
Received: September 15, 2017

Citation: Yu. N. Drozhzhinov, “Asymptotically homogeneous generalized functions and some of their applications”, Complex analysis, mathematical physics, and applications, Collected papers, Trudy Mat. Inst. Steklova, 301, MAIK Nauka/Interperiodica, Moscow, 2018, 74–90; Proc. Steklov Inst. Math., 301 (2018), 65–81

Citation in format AMSBIB
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  • Труды Математического института им. В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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