A discrete weighted Markov–Bernstein inequality for sequences and polynomials

2021 ◽  
Vol 493 (1) ◽  
pp. 124522
Author(s):  
Dimitar K. Dimitrov ◽  
Geno P. Nikolov
Keyword(s):  
Bernstein Inequality

scholarly journals On the Bernstein Inequality for Rational Functions with a Prescribed Zero

1998 ◽  
Vol 95 (3) ◽  
pp. 476-496 ◽  
Author(s):  
Roy Jones ◽  
Xin Li ◽  
R.N. Mohapatra ◽  
R.S. Rodriguez
Keyword(s):  
Rational Functions ◽  
Bernstein Inequality

scholarly journals Bernstein-type inequality for a class of dependent random matrices

2016 ◽  
Vol 05 (02) ◽  
pp. 1650006 ◽  
Author(s):  
Marwa Banna ◽  
Florence Merlevède ◽  
Pierre Youssef
Keyword(s):  
Random Matrices ◽  
Type Inequality ◽  
Bernstein Inequality ◽  
Mathematical Statistics ◽  
Strong Mixing ◽  
Mixing Conditions ◽  
Bernstein Type ◽  
Bernstein Type Inequality ◽  
The Matrix ◽  
The Laplace Transform

In this paper, we obtain a Bernstein-type inequality for the sum of self-adjoint centered and geometrically absolutely regular random matrices with bounded largest eigenvalue. This inequality can be viewed as an extension to the matrix setting of the Bernstein-type inequality obtained by Merlevède et al. [Bernstein inequality and moderate deviations under strong mixing conditions, in High Dimensional Probability V: The Luminy Volume, Institute of Mathematical Statistics Collection, Vol. 5 (Institute of Mathematical Statistics, Beachwood, OH, 2009), pp. 273–292.] in the context of real-valued bounded random variables that are geometrically absolutely regular. The proofs rely on decoupling the Laplace transform of a sum on a Cantor-like set of random matrices.

On the S. N. Bernstein Inequality

1971 ◽  
Vol 16 (1) ◽  
pp. 182-184
Author(s):  
S. L. Blyumin ◽  
B. D. Kotlyar
Keyword(s):  
Bernstein Inequality

scholarly journals Holonomic modules for rings of invariant differential operators

2021 ◽  
pp. 1-18
Author(s):  
Vyacheslav Futorny ◽  
João Schwarz
Keyword(s):  
Differential Operators ◽  
Main Tool ◽  
Bernstein Inequality ◽  
Invariant Differential Operators ◽  
Weyl Algebras ◽  
Invariant Differential ◽  
Quotient Varieties ◽  
Generalized Weyl Algebras ◽  
A Finite Group ◽  
Holonomic Modules

We study holonomic modules for the rings of invariant differential operators on affine commutative domains with finite Krull dimension with respect to arbitrary actions of finite groups. We prove the Bernstein inequality for these rings. Our main tool is the filter dimension introduced by Bavula. We extend the results for the invariants of the Weyl algebra with respect to the symplectic action of a finite group, for the rings of invariant differential operators on quotient varieties, and invariants of certain generalized Weyl algebras under the linear actions. We show that the filter dimension of all above mentioned algebras equals [Formula: see text].

scholarly journals Point-wise estimates for the derivative of algebraic polynomials

2021 ◽  
Vol 56 (2) ◽  
pp. 208-211
Author(s):  
A. V. Savchuk
Keyword(s):  
Algebraic Polynomial ◽  
Bernstein Inequality ◽  
Sufficient Condition ◽  
Algebraic Polynomials

We give a sufficient condition on coefficients $a_k$ of an algebraic polynomial $P(z)=\sum\limits_{k=0}^{n}a_kz^k$, $a_n\not=0,$ such that the pointwise Bernstein inequality $|P'(z)|\le n|P(z)|$ is true for all $z,\ |z|\le 1$.

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