Обсуждение:Неравенство Джексона — Стечкина

I believe Stechkin was hardly born when Jackson proved this ineq., any many more people - e.g. S.N.Bernstein - contributed to extensions. Therefore "Jackson ineq." is a proper name.

1) Jackson proved with constant 12 in a case of trigonometric polinomials in L^2. Stechkin proved with constant 3/2 and in much more general spaces. Most contributions to the inequality after Stechkin (including finding sharp constant 1/sqrt(2)) were maid by Stechkin's students and grandstudents, so a "Jackson-Stechkin inequality" is a quite common name in russian literature on the topic. So I didn't mention Stechkin in english wikipedia and mentioned him in russian.

2) Actually Jackson himself wasn't a first person who proved this type of inequality. I'll ask a specialists on the inequality when I'll meet them. Mir76 13:20, 7 февраля 2007 (UTC)

You see, as far as I know this is the common name in Russian literature after one of the "anti-cosmpopolitism" campaigns (in some of which Stechkin himself participated). The major contributions after Jackson were due, I believe, to de la Vallee Poussin, S.N.Bernstein (both worked before Stechkin), Akhiezer, Krein, Stechkin, ... (in approximately chronological order). Note by the way that the sharp constants appear already in Akhiezer's book on Approximation Theory (1-st edition: 1947), also before Stechkin's work. Therefore I am not quite sure about your historical account. Best, Sasha 01:09 8/2/2007

Can you read the article now? I have added some history including S.N.Bernstein. May be this will clear situation. And can you say a little bit more about Stechkin's "anti-cosmpopolitism" campaign? Mir76 13:16, 8 февраля 2007 (UTC)

Thanks, I will read it carefully and reply then.132.66.234.55 16:05, 8 февраля 2007 (UTC)