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 Ufimsk. Mat. Zh., 2013, Volume 5, Issue 1, Pages 17–35 (Mi ufa184)

Generalized functions asymptotically homogeneous with respect to one–parametric group at origin

Yu. N. Drozhzhinov, B. I. Zavialov

Steklov Mathematical Institute of the Russian Academy of Sciences

Abstract: In the work we obtain a complete description of generalized functions asymptotically homogeneous at origin w.r.t. a multiplicative one–parametric group of transformations so that the real parts of all the eigenvalues of infinitesimal matrix are positive including the case of critical orders. The obtained results are applied for constructing homogeneous solutions to differential equations whose symbols are quasi-homogeneous polynomials w.r.t. this group in a non-critical case.

Keywords: generalized functions, homogeneous functions, quasi-asymptotics, partial differential equations.

 Funding Agency Grant Number Ministry of Education and Science of the Russian Federation ÍØ 2928.2012.1 Russian Foundation for Basic Research 10-01-00178

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English version:
Ufa Mathematical Journal, 2013, 5:1, 17–35 (PDF, 422 kB); https://doi.org/10.13108/2013-5-1-17

Bibliographic databases:

UDC: 517.5

Citation: Yu. N. Drozhzhinov, B. I. Zavialov, “Generalized functions asymptotically homogeneous with respect to one–parametric group at origin”, Ufimsk. Mat. Zh., 5:1 (2013), 17–35; Ufa Math. J., 5:1 (2013), 17–35

Citation in format AMSBIB
\Bibitem{DroZav13} \by Yu.~N.~Drozhzhinov, B.~I.~Zavialov \paper Generalized functions asymptotically homogeneous with respect to one--parametric group at origin \jour Ufimsk. Mat. Zh. \yr 2013 \vol 5 \issue 1 \pages 17--35 \mathnet{http://mi.mathnet.ru/ufa184} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=3429948} \elib{http://elibrary.ru/item.asp?id=18929624} \transl \jour Ufa Math. J. \yr 2013 \vol 5 \issue 1 \pages 17--35 \crossref{https://doi.org/10.13108/2013-5-1-17} 

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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. Drozhzhinov Yu.N., Zav'yalov B.I., “Asymptotically Homogeneous Solutions of Differential Equations Whose Symbols Are Polynomials Quasi-Homogeneous with Respect to One-Parameter Groups with Generators Containing a Nilpotent Component”, Dokl. Math., 88:2 (2013), 590–592
2. Yu. N. Drozhzhinov, B. I. Zavialov, “Asymptotically homogeneous solutions to differential equations with homogeneous polynomial symbols with respect to a multiplicative one-parameter group”, Proc. Steklov Inst. Math., 285 (2014), 99–119
3. Yu. N. Drozhzhinov, “Asymptotically homogeneous generalized functions and some of their applications”, Proc. Steklov Inst. Math., 301 (2018), 65–81
4. S. Baizaev, M. A. Rakhimova, “Some functional equations in Schwartz space and their applications”, Ufa Math. J., 10:1 (2018), 3–13
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