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Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 2013, Issue 4, Pages 36–54 (Mi vuu400)  

This article is cited in 3 scientific papers (total in 3 papers)

MATHEMATICS

The uniform approximation of recurrent functions and almost recurrent functions

L. I. Danilov

Physical Technical Institute of Ural Branch of the Russian Academy of Sciences, ul. Kirova, 132, Izhevsk, 426000, Russia

Abstract: We consider the classes of functions $f\colon\mathbb R\to U$, taking values in a metric space $(U,\rho)$, which have Bochner transforms from the classes of recurrent functions and almost recurrent functions. We improve the preceding results on the uniform approximation of functions from classes under consideration by elementary functions from the same classes. These results can be applied to the investigation of the problem of the existence of almost recurrent selections for multivalued maps. The selections are supposed to satisfy a number of additional conditions. In the last section of the paper the variant of Lusin's theorem for recurrent functions is proved.

Keywords: recurrent function, selection, multivalued mapping, Lusin's theorem.

Full text: PDF file (309 kB)
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UDC: 517.518.6
MSC: 42A75, 54C65
Received: 30.10.2013

Citation: L. I. Danilov, “The uniform approximation of recurrent functions and almost recurrent functions”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 2013, no. 4, 36–54

Citation in format AMSBIB
\Bibitem{Dan13}
\by L.~I.~Danilov
\paper The uniform approximation of recurrent functions and almost recurrent functions
\jour Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki
\yr 2013
\issue 4
\pages 36--54
\mathnet{http://mi.mathnet.ru/vuu400}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. L. I. Danilov, “Rekurrentnye i pochti rekurrentnye mnogoznachnye otobrazheniya i ikh secheniya. III”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 2014, no. 4, 25–52  mathnet
    2. L. I. Danilov, “Rekurrentnye i pochti avtomorfnye secheniya mnogoznachnykh otobrazhenii”, Izv. IMI UdGU, 2015, no. 2(46), 45–52  mathnet  elib
    3. L. I. Danilov, “Shift dynamical systems and measurable selectors of multivalued maps”, Sb. Math., 209:11 (2018), 1611–1643  mathnet  crossref  crossref  adsnasa  isi  elib
  • Вестник Удмуртского университета. Математика. Механика. Компьютерные науки
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