Related papers: Demailly's approximation of general weights

We prove an easy statement about inhomogeneous approximation in metric theory of Diophantine Approximation.

We introduce a notion of quasi-weak equivalences associated with weak-equivalences in an exact category. It gives us a delooping for (idempotent complete) exact categories and a condition that the negative $K$-group of an exact category…

This paper evaluates some generalised Euler sums involving the digamma function.

We establish some new generalizations of Erd\H{o}s-Mordell inequality by adding weights to its terms. Using these generalizations, we derived strengthened versions of the original Erd\H{o}s-Mordell inequality. We also found two other…

We show that the sign constancy for the values of certain weighted summatory functions of the von Mangoldt function implies the Riemann hypothesis or the generalized Riemann hypothesis for Dirichlet $L$-functions. While such sign constancy…

We prove that a system of equations introduced by Demailly (to attack a conjecture of Griffiths) has a smooth solution for a direct sum of ample line bundles on a Riemann surface. We also reduce the problem for general vector bundles to an…

In this paper we investigate some strong convergence theorems for partial sums with respect to Vilenkin system.

We study the approximation of non-negative multi-variate couplings in the uniform norm while matching given single-variable marginal constraints.

Extending classical results on polytopal approximation of convex bodies, we derive asymptotic formulas for the weighted approximation of smooth convex functions by piecewise affine convex functions as the number of their facets tends to…

We approximate the solution to some linear and degenerate quasi-linear problem involving a linear elliptic operator (like the semi-discrete in time implicit Euler approximation of Richards and Stefan equations) with measure right-hand side…

This expository note aims at illustrating weak convergence of probability measures from a broader view than a previously published paper. Though the results are standard for functional analysts, this approach is rarely known by…

In this paper, approximate lower and upper Hermite--Hadamard type inequalities are obtained for functions that are approximately convex with respect to a given Chebyshev system.

In this note we study a quantitative version of Bernstein's approximation problem when the polynomials are dense in weighted spaces on the real line completing a result of S.~N.~Mergelyan (1960). We estimate in the logarithmic scale the…

In this paper, using some aspects of convex functions, we refine discrete Jensen's inequality via weight functions. Then, using these results, we give some applications in different abstract spaces and obtain some new interesting…

This paper is motivated by two problems in the theory of Diophantine approximation, namely, Davenport's problem regarding badly approximable points on submanifolds of a Euclidean space and Schmidt's problem regarding the intersections of…

An existence and uniqueness theorem for a class of stochastic delay differential equations is presented, and the convergence of Euler approximations for these equations is proved under general conditions. Moreover, the rate of almost sure…

We find asymptotic equalities for exact upper bounds of approximations by Fourier sums in uniform metric on classes of $2\pi$-periodic functions, representable in the form of convolutions of functions $\varphi$, which belong to unit balls…

In this article, we prove a weighted version of Saitoh's conjecture. As an application, we prove a weighted version of Saitoh's conjecture for higher derivatives.

In this paper we construct approximations for the Caputo derivative of order $1-\alpha,2-\alpha,2$ and $3-\alpha$. The approximations have weights $0.5\left((k+1)^{-\alpha}-(k-1)^{-\alpha}\right)/\Gamma(1-\alpha)$ and…

We give a fully algebraic proof of an important theorem of Demailly, stating the existence of many Green-Griffiths jet differentials on a complex projective manifold of general type. To this end, we introduce a new algebraic version of the…