Related papers: A note on Kronecker's approximation theorem
We survey the classical results of the Dirichlet Approximation Theorem.
We present a relative form of the Toponogov comparison theorem.
Approximations to the Kruskal-Katona theorem are stated and proven. These approximations are weaker than the theorem, but much easier to work with numerically.
This text is an appendix to our work "On the growth of Kronecker coefficients", arXiv:1607.02887. Here, we provide some complementary theorems, remarks, and calculations that for the sake of space are not going to appear into the final…
We improve constants in the Rademacher-Menchov inequality.
We present a short new proof of Cobham's theorem without using Kronecker's approximation theorem, making it suitable for generalization beyond automatic sequences.
We give an optimal version of the classical ``three-gap theorem'' on the fractional parts of $n \theta$, in the case where $\theta$ is an irrational number that is badly approximable. As a consequence, we deduce a version of Kronecker's…
We prove an easy statement about inhomogeneous approximation in metric theory of Diophantine Approximation.
In this paper, we give a counter-example, in the general case, Kronecker theorem will derive contradiction. Kronecker theorem be correct after removing some conditions.
An technically interesting proof of a known theorem.
A complete p-adic Khintchine type theorem for approximation by p-adic algebraic numbers is established.
We prove an analogue of the classical Bernstein theorem concerning the rate of polynomial approximation of piecewise analytic functions on a compact subset of the real line.
This paper is aimed to prove a quantitative estimate (in terms of the modulus of continuity) for the convergence in the nonlinear version of Korovkin's theorem for sequences of weakly nonlinear and monotone operators defined on spaces of…
We give some comments on W.M. Schmidt's theorem on Diophantine approximations with positive integers and our recent results on the topic.
We provide the detailed proof of a strengthened version of the M. Artin Approximation Theorem.
We make some observation on the logarithmic version of K-stability.
We seek random versions of some classical theorems on complex approximation by polynomials and rational functions, as well as investigate properties of random compact sets in connection to complex approximation.
The paper presents a counterexample to the Hodge conjecture.
In this short note we have proved an enhanced version of a theorem of Lorentz [1] and its generalization to the multivariate case which gives a non- uniform estimate of degree of approximation by a polynomial with positive coefficients. The…
We prove a limit theorem for quantum stochastic differential equations with unbounded coefficients which extends the Trotter-Kato theorem for contraction semigroups. From this theorem, general results on the convergence of approximations…