A counterexample to Ljamin's theorem

Piotr Maćkowiak

Abstract

One of the well-known results ensuring that a nonautonomous superposition operator maps the set of functions of one variable of bounded variation in the sense of Jordan into itself is the theorem by A. G. Ljamin. According to that theorem it suffices to consider the class of functions which are uniformly Lipschitz w.r.t. the second variable and of uniformly bounded variation w.r.t. the first variable. Unfortunately, Ljamin's result is false. Here we deliver an example contradicting sufficiency of those conditions.
Author Piotr Maćkowiak (WIiGE / KEM)
Piotr Maćkowiak,,
- Department of Mathematical Economics
Journal seriesProceedings of the American Mathematical Society, ISSN 0002-9939, (A 25 pkt)
Issue year2014
Vol142
No5
Pages1773-1776
Publication size in sheets0.5
Keywords in EnglishNonautonomous superposition operator, functions of bounded variation in the sense of Jordan
ASJC Classification2600 General Mathematics; 2604 Applied Mathematics
DOIDOI:10.1090/S0002-9939-2014-11912-5
URL http://www.ams.org/journals/proc/2014-142-05/S0002-9939-2014-11912-5/
Languageen angielski
Score (nominal)25
Score sourcejournalList
ScoreMinisterial score = 25.0, 13-12-2019, ArticleFromJournal
Ministerial score (2013-2016) = 25.0, 13-12-2019, ArticleFromJournal
Publication indicators WoS Citations = 5; Scopus SNIP (Source Normalised Impact per Paper): 2014 = 1.093; WoS Impact Factor: 2014 = 0.681 (2) - 2014=0.68 (5)
Citation count*8 (2020-08-10)
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* presented citation count is obtained through Internet information analysis and it is close to the number calculated by the Publish or Perish system.
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