Related papers: Bernstein- and Markov-type inequalities for ration…
We consider additive functionals of stationary Markov processes and show that under Kipnis-Varadhan type conditions they converge in rough path topology to a Stratonovich Brownian motion, with a correction to the Levy area that can be…
We study the rational approximation properties of special manifolds defined by a set of polynomials with rational coefficients. Mostly we will assume the case of all polynomials to depend on only one variable. In this case the manifold can…
Our goal is to find asymptotic formulas for orthonormal polynomials $P_{n}(z)$ with the recurrence coefficients slowly stabilizing as $n\to\infty$. To that end, we develop spectral theory of Jacobi operators with long-range coefficients and…
We obtain approximation results for general positive linear operators satisfying mild conditions, when acting on discontinuous functions and absolutely continuous functions having discontinuous derivatives. The upper bounds, given in terms…
We prove a flatness result for entire nonlocal minimal graphs having some partial derivatives bounded from either above or below. This result generalizes fractional versions of classical theorems due to Bernstein and Moser. Our arguments…
When $A=3$, the positive integral solutions of the so-called Markoff equation $$M_A:x^2 + y^2 + z^2 = Axyz$$ can be generated from the single solution $(1,1,1)$ by the action of certain automorphisms of the hypersurface. Since Markoff's…
We derive explicit formulas for the Arakelov-Green function and the Faltings delta-invariant of a Riemann surface. A numerical example illustrates how these formulas can be used to calculate Arakelov invariants of curves.
We prove a duality theorem the computation of certain Bellman functions is usually based on. As a byproduct, we obtain sharp results about the norms of monotonic rearrangements. The main novelty of our approach is a special class of…
In this paper we show that the weighted Bernstein-Walsh inequality in logarithmic potential theory is sharp up to some new universal constant, provided that the external field is given by a logarithmic potential. Our main tool for such…
A Bernstein-type exponential inequality for (generalized) canonical U-statistics of order 2 is obtained and the Rosenthal and Hoffmann-J{\o}rgensen inequalities for sums of independent random variables are extended to (generalized)…
In this paper, we obtain some Simpson type inequalities for functions whose second derivatives absolute value or q-th power of them are Q-class functions. Also we give applications to numerical integration.
We establish the existence, uniqueness, and various estimates for Green functions of mixed Dirichlet-conormal derivative problems for the stationary Stokes system with measurable coefficients in a two-dimensional Reifenberg flat domain with…
This paper establishes a sharp Schwarz-Pick type inequality for real-valued invariant harmonic functions defined on the complex unit ball $\mathbb B^n$. The proof of this main result simultaneously provides a solution to a natural extension…
Let $V\subset\R^m$ be a convex body, symmetric about all coordinate hyperplanes, and let $\PP_{aV},\, a\ge 0$, be a set of all algebraic polynomials whose Newton polyhedra are subsets of $aV$. We prove a limit equality as $a\to \iy$ between…
Green's conjecture is proved for smooth curves C lying on a rational surface S with an anticanonical pencil, under some mild hypotheses on the line bundle L defined by C. Constancy of Clifford dimension, Clifford index and gonality of…
In this paper, two double Jordan-type inequalities are introduced that generalize some previously established inequalities. As a result, some new upper and lower bounds and approximations of the sinc function are obtained. This extension of…
This note contains some estimates for tail spaces on Hamming cube. We use analytic paraproduct operator for that purpose. We also show several types of Bernstein--Markov inequalities for Banach space valued functions on Hamming cube. Here…
We generalize the classical Bernstein theorem concerning the constructive description of classes of functions uniformly continuous on the real line. The approximation of continuous bounded functions by entire functions of exponential type…
Some Tur\'an type inequalities for Struve functions of the first kind are deduced by using various methods developed in the case of Bessel functions of the first and second kind. New formulas, like Mittag-Leffler expansion, infinite product…
For any complex $\alpha$ with non-zero imaginary part we show that Bernstein-Walsh type inequality holds on the piece of the curve $\{(e^z,e^{\alpha z}) : z \in \mathbb C\}$. Our result extends a theorem of Coman-Poletsky \cite{CP10} where…