Related papers: Almost everywhere Convergence of Spline Sequences

Let $\displaystyle \{x_{k,n-1}\} _{k=1}^{n-1}$ and $\displaystyle \{x_{k,n}\} _{k=1}^{n},$ $n \in \mathbb{N}$, be two sets of real, distinct points satisfying the interlacing property $ x_{i,n}<x_{i,n-1}< x_{i+1,n}, \, \, \, i =…

It is a classical fact that domains of convergence of power series of several complex variables are characterized as logarithmically convex complete Reinhardt domains; let $D \subsetneq \mathbb{C}^N$ be such a domain. We show that a…

Let $P$ be a finite point set in $\mathbb{R}^2$ with the set of distance $n$-chains defined as $$ \Delta_n(P)=\{(|p_1-p_2|,|p_2-p_3|,\ldots,|p_n-p_{n+1}|):p_i \in P\}.$$ We show that for $2\leq n=O_{|P|}(1)$ we have $$|\Delta_n(P)|\gtrsim…

We construct an analogue of the Lyndon-Hochschild-Serre spectral sequence in the context of polynomial cohomology, for group extensions. If G is an extension of Q by H, then the spectral sequence converges to the polynomial cohomology of G.…

In this note we explore the notion of everywhere almost summing polynomials and define a natural norm which makes this class a Banach multi-ideal which is a holomorphy type (in the sense of L.Nachbin) and also coherent and compatible (in…

We describe an action of the concordance group of knots in the three-sphere on concordances of knots in arbitrary 3-manifolds. As an application we define the notion of almost-concordance between knots. After some basic results, we prove…

Let $X$ be a Banach space and $(f_n)_n$ be a bounded sequence in $L^1(X)$. We prove a complemented version of the celebrated Talagrand's dichotomy i.e we show that if $(e_n)_n$ denotes the unit vector basis of $c_0$, there exists a sequence…

Let $\Lambda \subset \mathbb R^n$ be an algebraic lattice, coming from a projective module over the ring of integers of a number field $K$. Let $\mathcal Z \subset \mathbb R^n$ be the zero locus of a finite collection of polynomials such…

We introduce and study the approximation properties of $g$-polynomials, defined as linear combinations of iterated Stieltjes integrals of a constant function. Focusing on the case where the derivator $g$ has finitely many discontinuities,…

Let x be a quadratic irrational and let P be the set of prime numbers. We show the existence of an infinite subset S of P such that the statistics of the period of the continued fraction expansions along the sequence {px: p\in S} approach…

We show that an arbitrary nilprogression can be approximated by a proper coset nilprogression in upper-triangular form. This can be thought of as a nilpotent version of the Freiman-Bilu result that a generalised arithmetic progression can…

We study the minimization of fixed-degree polynomials over the simplex. This problem is well-known to be NP-hard, as it contains the maximum stable set problem in graph theory as a special case. In this paper, we consider a rational…

We prove that for a sufficiently ample line bundle $L$ on a surface $S$, the number of $\delta$-nodal curves in a general $\delta$-dimensional linear system is given by a universal polynomial of degree $\delta$ in the four numbers…

We consider a large class of piecewise expanding maps T of [0,1] with a neutral fixed point, and their associated Markov chain Y_i whose transition kernel is the Perron-Frobenius operator of T with respect to the absolutely continuous…

Assuming that $\phi(t)=o(t^2)$ as $t\to0$, we establish a lemma on simultaneous polynomial approximation in Orlicz-Beurling-Sobolev spaces $\ell_a^{\phi}$. These spaces, endowed with the Luxemburg norm $\Vert \cdot \Vert_{\ell^{\phi}}$,…

In this paper we show that, if an increasing sequence $\Lambda=(\lambda_k)_{k\in\mathbb{Z}}$ has gaps going to infinity $\lambda_{k+1}-\lambda_k\to +\infty$ when $k\to\pm\infty$, then for every $T>0$ and every sequence…

Recently, an analogue over $\mathbb{F}_q[T]$ of Landau's theorem on sums of two squares was considered by Bary-Soroker, Smilansky and Wolf. They counted the number of monic polynomials in $\mathbb{F}_q[T]$ of degree $n$ of the form…

We provide a convergence result for sequences of random variables taking values in a metric space that satisfy a stochastic quasi-Fej\'er monotonicity condition, in the context of a (local) compactness assumption. Our result is quantitative…

The model theory based notion of the first order convergence unifies the notions of the left-convergence for dense structures and the Benjamini-Schramm convergence for sparse structures. It is known that every first order convergent…

Let S be a complex smooth projective surface and L be a line bundle on S. G\"ottsche conjectured that for every integer r, the number of r-nodal curves in |L| is a universal polynomial of four topological numbers when L is sufficiently…