scholarly journals Asymptotics of sharp constants of Markov-Bernstein inequalities in integral norm with Jacobi weight

2015 ◽  
Vol 143 (9) ◽  
pp. 3847-3862 ◽  
Author(s):  
A. I. Aptekarev ◽  
A. Draux ◽  
V. A. Kalyagin ◽  
D. N. Tulyakov
Keyword(s):  
Sharp Constants ◽  
Integral Norm ◽  
Jacobi Weight ◽  
Bernstein Inequalities

On the asymptotics of sharp constants in Markov-Bernstein inequalities in integral metrics with classical weight

2000 ◽  
Vol 55 (1) ◽  
pp. 163-165 ◽  
Author(s):  
A I Aptekarev ◽  
A Draux ◽  
V A Kalyagin
Keyword(s):  
Sharp Constants ◽  
Integral Metrics ◽  
Bernstein Inequalities

Generalized qd algorithm and Markov–Bernstein inequalities for Jacobi weight

2008 ◽  
Vol 51 (4) ◽  
pp. 429-447 ◽  
Author(s):  
André Draux ◽  
Borhane Moalla ◽  
Mohamed Sadik
Keyword(s):  
Jacobi Weight ◽  
Bernstein Inequalities

scholarly journals Bernstein inequalities via the heat semigroup

2021 ◽  
Author(s):  
Rafik Imekraz ◽  
El Maati Ouhabaz
Keyword(s):  
Heat Semigroup ◽  
Bernstein Inequalities

Functional calculus of Hermitian elements and Bernstein inequalities

2006 ◽  
Vol 40 (2) ◽  
pp. 148-150 ◽  
Author(s):  
S. Norvidas
Keyword(s):  
Functional Calculus ◽  
Bernstein Inequalities

SOME ESTIMATES FOR POLYNOMIALS

2009 ◽  
Vol 02 (03) ◽  
pp. 425-434
Author(s):  
Tatsuhiro Honda ◽  
Mitsuhiro Miyagi ◽  
Masaru Nishihara ◽  
Seiko Ohgai ◽  
Mamoru Yoshida
Keyword(s):  
Trigonometric Polynomials ◽  
Alternative Proof ◽  
Bernstein Inequalities

We give an elementary alternative proof of the Bernstein inequalities and the Szegö inequalities for trigonometric polynomials or polynomials.

Exceptional solutions to the Painlevé VI equation associated with the generalized Jacobi weight

2017 ◽  
Vol 06 (01) ◽  
pp. 1750003
Author(s):  
Shulin Lyu ◽  
Yang Chen
Keyword(s):  
Asymptotic Expansions ◽  
Hankel Determinant ◽  
Generalized Jacobi Weight ◽  
Jacobi Weight ◽  
Special Cases ◽  
Painlevé Vi Equation

We consider the generalized Jacobi weight [Formula: see text], [Formula: see text]. As is shown in [D. Dai and L. Zhang, Painlevé VI and Henkel determinants for the generalized Jocobi weight, J. Phys. A: Math. Theor. 43 (2010), Article ID:055207, 14pp.], the corresponding Hankel determinant is the [Formula: see text]-function of a particular Painlevé VI. We present all the possible asymptotic expansions of the solution of the Painlevé VI equation near [Formula: see text] and [Formula: see text] for generic [Formula: see text]. For four special cases of [Formula: see text] which are related to the dimension of the Hankel determinant, we can find the exceptional solutions of the Painlevé VI equation according to the results of [A. Eremenko, A. Gabrielov and A. Hinkkanen, Exceptional solutions to the Painlevé VI equation, preprint (2016), arXiv:1602.04694 ], and thus give another characterization of the Hankel determinant.

𝐿^{𝑝}-Bernstein inequalities on 𝐶²-domains and applications to discretization

2021 ◽  
Author(s):  
Feng Dai ◽  
Andriy Prymak
Keyword(s):  
Bernstein Inequalities

General sharp weighted Caffarelli–Kohn–Nirenberg inequalities

2018 ◽  
Vol 149 (03) ◽  
pp. 691-718 ◽  
Author(s):  
Nguyen Lam
Keyword(s):  
Mass Transport ◽  
Sharp Constants ◽  
Optimal Mass Transport

AbstractIn this paper, we will use optimal mass transport combining with suitable transforms to study the sharp constants and optimizers for a class of the Gagliardo–Nirenberg and Caffarelli–Kohn–Nirenberg inequalities. Moreover, we will investigate these inequalities with and without the monomial weights $x_{1}^{A_{1}} \cdots x_{N}^{A_{N}}$ on ℝN.

SHARP POINCARÉ–SOBOLEV INEQUALITIES AND THE SHORTEST LENGTH OF SIMPLE CLOSED GEODESICS ON A TOPOLOGICAL TWO SPHERE

2004 ◽  
Vol 06 (05) ◽  
pp. 781-792 ◽  
Author(s):  
MEIJUN ZHU
Keyword(s):  
Riemannian Manifold ◽  
Sobolev Inequalities ◽  
Square Root ◽  
Two Dimensional ◽  
Closed Geodesics ◽  
Sharp Constants ◽  
Simple Closed Geodesics

We show that the sharp constants of Poincaré–Sobolev inequalities for any smooth two dimensional Riemannian manifold are less than or equal to [Formula: see text]. For a smooth topological two sphere M2, the sharp constants are [Formula: see text] if and only if M2 is isometric to two sphere S2 with the standard metric. In the same spirit, we show that for certain special smooth topological sphere the ratio between the shortest length of simple closed geodesics and the square root of its area is less than or equals to [Formula: see text].

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