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Mat. Zametki, 1969, Volume 6, Issue 4, Pages 361–369 (Mi mz6942)  

This article is cited in 1 scientific paper (total in 1 paper)

Necessary and sufficient conditions for the linearity of transformations which preserve cones

R. I. Pimenov

Leningrad Department of V. A. Steklov Institute of Mathematics, USSR Academy of Sciences

Abstract: We find a criterion for the linearity of mappings, preserving equal and parallel cones, in one of the exceptional cases to which the theorem of A. D. Aleksandrov does not extend.

Full text: PDF file (733 kB)

English version:
Mathematical Notes, 1969, 6:4, 675–679

Bibliographic databases:

UDC: 513.78
Received: 07.05.1968

Citation: R. I. Pimenov, “Necessary and sufficient conditions for the linearity of transformations which preserve cones”, Mat. Zametki, 6:4 (1969), 361–369; Math. Notes, 6:4 (1969), 675–679

Citation in format AMSBIB
\Bibitem{Pim69}
\by R.~I.~Pimenov
\paper Necessary and sufficient conditions for the linearity of transformations which preserve cones
\jour Mat. Zametki
\yr 1969
\vol 6
\issue 4
\pages 361--369
\mathnet{http://mi.mathnet.ru/mz6942}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=251622}
\zmath{https://zbmath.org/?q=an:0189.52902|0186.55702}
\transl
\jour Math. Notes
\yr 1969
\vol 6
\issue 4
\pages 675--679
\crossref{https://doi.org/10.1007/BF01093800}


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    This publication is cited in the following articles:
    1. R. A. Bogdanova, “Gruppa dvizhenii simplitsialnoi ploskosti kak reshenie funktsionalnogo uravneniya”, Vestn. Tomsk. gos. un-ta. Matem. i mekh., 2014, no. 4(30), 5–13  mathnet
  • Математические заметки Mathematical Notes
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