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 ...

‎It is well known that every (real or complex) normed linear space $L$ is isometrically embeddable into $C(X)$ for some compact Hausdorff space $X$‎. ‎Here $X$ is the closed unit ball of $L^*$ (the set of all continuous scalar-valued linear mappings on $L$) endowed with the weak$^*$ topology‎, ‎which is compact by the Banach--Alaoglu theorem‎. ‎We prove that the compact Hausdorff space $X$ can ...

During recent decades, there have been a great number of research articles studying interior-point methods for solving problems in mathematical programming and constrained optimization. Stewart and O'Leary obtained an upper bound for scaled pseudoinverses sup W2P k(W 1 2 X) + W 1 2 k 2 of a matrix X where P is a set of diagonal positive deenite matrices. We improved their results to obtain the ...

A notion of detectability for nonlinear systems is discussed. Within the framework of “input to state stability” (ISS), a dual notion of “output to state stability” (OSS), and a more complete detectability notion, “input-output to state stability” (IOSS) have appeared in the literature. This note addresses a variant of the IOSS property, using an integral norm to measure signals, as opposed to ...

Let E be the union of two real intervals not containing zero. Then Ln(E) denotes the supremum norm of that polynomial Pn of degree less than or equal to n, which is minimal with respect to the supremum norm provided that Pn(0) = 1. It is well known that the limit κ(E) := limn→∞ n √ Ln(E) exists, where κ(E) is called the asymptotic convergence factor, since it plays a crucial role for certain it...

In this paper, a parameter uniform numerical method based on Shishkin mesh is suggested to solve a system of second order singularly perturbed differential equations with a turning point exhibiting boundary layers. It is assumed that both equations have a turning point at the same point. An appropriate piecewise uniform mesh is considered and a classical finite difference scheme is applied on t...

in the present paper, we introduce some new sequence spaces derived by riesz mean and the notions of almost and strongly almost convergence in a real 2-normed space. some topological properties of these spaces are investigated. further, new concepts of statistical convergence which will be called weighted almost statistical convergence, almost statistical convergence and statistical convergence...