Related papers: On Bernstein-type theorems
We obtain a fully explicit quantitative version of the Eisenstein theorem on algebraic power series which is more suitable for certain applications than the existing version due to Dwork, Robba, Schmidt and van der Poorten. We also treat…
We give derivations of some basic results for the Bernstein approximation in $n$ variables that are useful in investigating copulas. It is shown that Bernstein approximations of copulas are again copulas. We exhibit a stochastic…
We provide some new results of the ground state of quantum layers.
We introduce the degenerate Bernoulli numbers of the second kind as a degenerate version of the Bernoulli numbers of the second kind. We derive a family of nonlinear differential equations satisfied by a function closely related to the…
We establish a strong unique continuation property for stochastic parabolic equations. Our method is based on a suitable stochastic version of Carleman estimate. As far as we know, this is the first result for strong unique continuation…
Let $k$ be a differential field of characteristic zero with an algebraically closed field of constants. In this article, we provide a classification of first order differential equations over $k$ and study the algebraic dependence of…
We consider a variational problem with boundary singularity and Dirichlet condition. We give a blow-up analysis for sequences of solutions of an equation with exponential nonlinearity. Also, we derive a compactness criterion under some…
We derive "numerical" criteria for the existence of embeddings of representations of finite dimensional algebras.
We establish the existence of the Bernstein polynomial in one indeterminate $t$, and provide a method for its explicit computation. The Bernstein polynomial is associated with finitely generated modules over the Weyl algebra, known as…
We are concerned with existence results for a critical problem of Brezis-Nirenberg Type involving an integro-differential operator. Our study includes the fractional Laplacian. Our approach still applies when adding small singular terms. It…
A family of nonlinear partial differential equations of divergence form is considered. Each one is the Euler-Lagrange equation of a natural Riemaniann variational problem of geometric interest. New uniqueness results for the entire…
We improve on Gonek-Montgomery's quantitative version of Kronecker's approximation theorem.
This paper considers the properties of Tribonacci numbers on identities, matrices, and determinants. In the first front part, we obtain several symmetric identities of Tribonacci numbers by a matrix-based approach and binomial inversion…
We show that a certain optimality property of the classical Bernstein operator also holds, when suitably reinterpreted, for generalized Bernstein operators on extended Chebyshev systems.
Characterization theorems for Q-independent random variables in Banach spaces
We present a review of recent work on the mathematical aspects of the BCS gap equation, covering our results of [arXiv:0801.4159] as well our recent joint work with Hamza and Solovej [arXiv:math-ph/0703086] and with Frank and Naboko…
Two types of Bernstein inequalities are established on the unit ball in $\mathbb{R}^d$, which are stronger than those known in the literature. The first type consists of inequalities in $L^p$ norm for a fully symmetric doubling weight on…
We prove some basic properties of quasinearly subharmonic functions and quasinearly subharmonic functions in the narrow sense.
We derive a separability criterion for bipartite quantum systems which generalizes the already known criteria. It is based on observables having generic commutation relations. We then discuss in detail the relation among these criteria.
In this paper, we investigate some properties of Chebyshev polynomials arising from non-linear differential equations. From our investigation, we derive some new and interesting identities on Chebyshev polynomials.