A counterexample to Ljamin's theorem
AbstractOne 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.
|Journal series||Proceedings of the American Mathematical Society, ISSN 0002-9939, (A 25 pkt)|
|Publication size in sheets||0.5|
|Keywords in English||Nonautonomous superposition operator, functions of bounded variation in the sense of Jordan|
|Score|| = 25.0, 13-12-2019, ArticleFromJournal|
= 25.0, 13-12-2019, ArticleFromJournal
|Publication indicators||= 5; : 2014 = 1.093; : 2014 = 0.681 (2) - 2014=0.68 (5)|
|Citation count*||9 (2021-06-07)|
* presented citation count is obtained through Internet information analysis and it is close to the number calculated by the Publish or Perish system.