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Funktsional'nyi Analiz i ego Prilozheniya, 2006, Volume 40, Issue 3, Pages 44–52
DOI: https://doi.org/10.4213/faa742 (Mi faa742) 		 
This article is cited in 3 scientific papers (total in 3 papers)

Local Smoothing of Uniformly Smooth Maps

I. G. Tsar'kov

M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
Full-text PDF (196 kB) Citations (3)
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DOI: https://doi.org/10.4213/faa742
Abstract: We solve the problem on the uniform approximation of uniformly continuous (smooth) maps by maps having the maximum possible local and uniform smoothness. In particular, we prove that each uniformly continuous map of the Hilbert space $l_2$ into itself can be approximated by locally infinitely differentiable maps having a Lipschitz derivative.
Keywords: approximation, smoothing, local smoothness, uniform smoothness, Lipschitz derivative.
Received: 30.11.2004
English version:
Functional Analysis and Its Applications, 2006, Volume 40, Issue 3, Pages 200–206
DOI: https://doi.org/10.1007/s10688-006-0031-2
Bibliographic databases:
Document Type: Article
UDC: 517.17
Language: Russian
Citation: I. G. Tsar'kov, “Local Smoothing of Uniformly Smooth Maps”, Funktsional. Anal. i Prilozhen., 40:3 (2006), 44–52; Funct. Anal. Appl., 40:3 (2006), 200–206
Citation in format AMSBIB
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    • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Функциональный анализ и его приложения Functional Analysis and Its Applications
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