Introduction. Let G be an open subset of the Euclidean w-space E, Gi an open subset with compact closure in G. If n = 2 and G is the whole of E, an important circle of theorems in the theory of analytic functions associated with the names of Walsh, HartogsRosenthal, Lavrentiev, Keldych, and Mergelyan deals with the possibility of approximating analytic functions on Gi continuous on its closure,...

We study the recovery of multivariate functions from reproducing kernel Hilbert spaces in uniform norm. Surprisingly, a certain weighted least squares operator which uses random samples tailored distribution leads to near-optimal results several relevant situations. The are stated terms decay related singular numbers compact embedding into $L_2(D)$ multiplied with supremum Christoffel function ...

Let vi be vectors in Rd and {εi} independent Rademacher random variables. Then the Littlewood–Offord problem entails finding best upper bound for supx∈RdP(∑εivi=x). Generalizing uniform bounds of Littlewood–Offord, Erdős Kleitman, a recent result Dzindzalieta Juškevičius provides non-uniform that is optimal its dependence on ‖x‖2. In this short note, we provide simple alternative proof their re...

In this paper, we concentrate our attention on the Müntz problem in the univariate setting and for the uniform norm. MSC: 41-01, 41-02

We investigate the robust PCA problem of decomposing an observed matrix into the sum of a low-rank and a sparse error matrices via convex programming Principal Component Pursuit (PCP). In contrast to previous studies that assume the support of the error matrix is generated by uniform Bernoulli sampling, we allow non-uniform sampling, i.e., entries of the low-rank matrix are corrupted by errors ...

We study the asymptotic structure of polynomials with integer coef cients and smallest uniform norms on an interval of the real line Introducing methods of the weighted potential theory into this problem we improve the bounds for the multiplicities of some factors of the integer Chebyshev polynomials Introduction Let Pn C and Pn Z be the sets of algebraic polynomials of degree at most n respect...

We show uniform convergence in the energy norm for an automatic hp-adaptive refinement strategy for the finite element method applied to Maxwell’s equations.

3 Uniform measures of complexity 12 3.1 Metric entropy and the combinatorial dimension . . . . . . . . . 12 3.1.1 Binary valued classes . . . . . . . . . . . . . . . . . . . . . 13 3.1.2 Real valued classes . . . . . . . . . . . . . . . . . . . . . . 15 3.2 Random averages and the combinatorial dimension . . . . . . . . 17 3.3 Phase transitions in GC classes . . . . . . . . . . . . . . . . . . ...

A strong error estimate for the uniform rational approximation of xa on [0, 1] is given, and its proof is sketched. Let E„n(xa, [0, 1]) denote the minimal approximation error in the uniform norm. Then it is shown that lim e2*^"Enn(xa , [0, 1]) = 41+a| sin7ta| n—»oo holds true for each a > 0 .

We give a new generalization of Bleimann, Butzer, and Hahn operators, which includes qintegers.We investigate uniform approximation of these new operators on some subspace of bounded and continuous functions. In Section 3, we show that the rates of convergence of the new operators in uniform norm are better than the classical ones. We also obtain a pointwise estimation in a general Lipschitz-ty...