|
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.
Keywords:
generalized functions, homogeneous functions, quasiasymptotics, partial differential equations.
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
Linking options:
https://www.mathnet.ru/eng/tm3899https://doi.org/10.1134/S0371968518020061 https://www.mathnet.ru/eng/tm/v301/p74
|
|