Remarks, questions and conjectures on Landau-Kolmogorov-type inequalities
نویسندگان
چکیده
منابع مشابه
Landau-Kolmogorov type inequalities for the Hermite and closely connected measures
Different types of polynomial inequalities have been studied since more one century. The first type is the so-called Markov-Bernstein inequalities (A. A. Markov in 1889 [5]). More recently other inequalities involving the Lnorm for the Hermite measure were given (see Bojanov and Varma [2], Alves and Dimitrov [1]). Inequalities given in the previous papers are particular cases of the more genera...
متن کاملLandau and Kolmogoroff Type Polynomial Inequalities
Let 0 < j < m ≤ n be integers. Denote by ‖ · ‖ the norm ‖f‖2 = ∫∞ −∞ f 2(x) exp(−x2)dx. For various positive values of A and B we establish Kolmogoroff type inequalities ‖f ‖ ≤ A‖f (m)‖2 +B‖f‖2 Aθk +Bμk , with certain constants θk e μk, which hold for every f ∈ πn (πn denotes the space of real algebraic polynomials of degree not exceeding n). For the particular case j = 1 and m = 2, we provide ...
متن کاملLandau and Kolmogoroff Type Polynomial Inequalities CLAUDIA
Reprints available directly from the publisher Photocopying permitted by license only (C) 1999 OPA (Overseas Publishers Association) N.V. Let 0 <j < m _< n be integers. Denote by I1" the norm Ilfll f2 f2(x) exp(-x2) dx. For various positive values of A and B we establish Kolmogoroff type inequalities ilfU) < , Ill (m) + BIIfll AOk + B#k with certain constants Oke lZk, which hold for every fE 7r...
متن کاملKolmogorov-Landau Functions
‖f ‖ ≤ Crq ‖f‖ 1−q/r ‖f ‖ was proved by Kolmogorov in [11] for f ∈W r ∞(R). Here ‖ · ‖ means ‖ · ‖L∞(R) and the sharp constant Crq = Kr−qK −1+q/r r is given in terms of the Favard constants Kp := 4 π ∑∞ n=0 [ (−1) 2n+1 p+1 . For the definition of the Sobolev space W r ∞(R) see e.g. [4, Ch. 1.5]. The first results of this type (the case q = 1, r = 2) were obtained by Hadamard in [9] and by Landa...
متن کاملSome Remarks on Landau-siegel Zeros
In this paper we show that, under the assumption that all the zeros of the L-functions under consideration are either real or lie on the critical line, one may considerably improve on the known results on Landau-Siegel zeros.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Mathematical Inequalities & Applications
سال: 2000
ISSN: 1331-4343
DOI: 10.7153/mia-03-02