Asymptotically homogeneous solutions to differential equations with homogeneous polynomial symbols with respect to a multiplicative one-parameter group
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We study solutions to partial differential equations with homogeneous polynomial symbols with respect to a multiplicative one-parameter transformation group such that all eigenvalues of the infinitesimal matrix are positive. The infinitesimal matrix may contain a nilpotent part. In the asymptotic scale of regularly varying functions, we find conditions under which such differential equations have asymptotically homogeneous solutions in the critical case.
KeywordsGeneralize Function STEKLOV Institute Homogeneous Polynomial Tauberian Theorem Positive Continuous Function
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- 6.I. M. Gel’fand and G. E. Shilov, Generalized Functions and Operations on Them (Fizmatgiz, Moscow, 1959); Engl. transl: Generalized Functions, Vol. 1: Properties and Operations (Academic, New York, 1964).Google Scholar