相关论文: The de la Vallee Poussin mean and polynomial appro…
In this paper, we discuss derivative of the de la Vallee Poussin mean for exponential weights on real line. When we lead an inequality, an estimate for the Christoffel function plays an important role.
H. N. Mhaskar obtained the inequalities for derivative of polynomial approximation with Freud type weight. In this paper, we showed the counterpart of the inequalities with Erdos type weight.
In this paper, we prove a quantitative approximation result by orthonormal polynomials associated to an exponential weight of the form e -$\Phi$ , where $\Phi$ is an even polynomial with positive leading coefficient. This result is a…
We study linear polynomial approximation of functions in weighted Sobolev spaces $W^r_{p,w}(\mathbb{R}^d)$ of mixed smoothness $r \in \mathbb{N}$, and their optimality in terms of Kolmogorov and linear $n$-widths of the unit ball…
We show that for multivariate Freud-type weights $W_\alpha(x)=\exp(-|x|^\alpha)$, $\alpha>1$, any convex function $f$ on $R^d$ satisfying $fW_\alpha\in L_p(R^d)$ if $1\le p<\infty$, or $\lim_{|x|\to\infty}f(x)W_\alpha(x)=0$ if $p=\infty$,…
In this note we study a quantitative version of Bernstein's approximation problem when the polynomials are dense in weighted spaces on the real line completing a result of S.~N.~Mergelyan (1960). We estimate in the logarithmic scale the…
In this paper there are several results, we prove approximation of periodic function by Fejer means and De La Vallee Poussin means in Lebesgue spaces the estimates are given in terms of function for and in terms of second continuity…
In this paper, we consider norm convergence for a special matrix-based de la Vall\'ee Poussin-like mean of Fourier series for the Walsh system. We estimate the difference between the named mean above and the corresponding function in norm,…
The theory of Chebyshev approximation has been extensively studied. In most cases, the optimality conditions are based on the notion of alternance or alternating sequence (that is, maximal deviation points with alternating deviation signs).…
We estimate short exponential sums weighted by the Fourier coefficients of a Maass form. This requires working out a certain transformation formula for non-linear exponential sums, which is of independent interest. We also discuss how the…
Both the mean square polynomial stability and exponential stability of $\theta$ Euler-Maruyama approximation solutions of stochastic differential equations will be investigated for each $0\le\theta\le 1$ by using an auxiliary function $F$…
On the half line we introduce a new sequence of near--best uniform approximation polynomials, easily computable by the values of the approximated function at a truncated number of Laguerre zeros. Such approximation polynomials come from a…
Let W: R to (0,1] be continuous. Bernstein's approximation problem, posed in 1924, deals with approximation by polynomials in the weighted uniform norm ||fW|| Linfinity(R) . The qualitative form of this problem was solved by Achieser,…
First we prove a modified version of the famous Lemma on the mean square estimate for exponential sums, by plugging the Cesaro weights in the right hand side of Gallagher's inequality. Then we apply it, in order to establish a mean value…
Let $\mathbb{R}=(-\infty,\infty)$, and let $Q\in C^1(\mathbb{R}): \mathbb{R}\rightarrow[0,\infty)$ be an even function. We consider the exponential weights $w(x)=e^{-Q(x)}$, $x\in \mathbb{R}$. In this paper we obtain a pointwise convergence…
We consider the problem of approximation of a continuous function $f$ defined on a compact metric space $X$ by elements from a sum of two algebras. We prove a de la Vall\'{e}e Poussin type theorem, which estimates the approximation error…
We study the polynomial approximation problem in $L^2(\mu_1)$ where $\mu_1(dx) = e^{-|x|}/2 dx$. We show that for any absolutely continuous function $f$, $$ \sum_{k=1}^{\infty} \log^2(e+k) \langle f, P_k \rangle^2 \ \leq C \left(…
We obtain the estimates of steady rates of deviations of the de Vall\'{e}e Poussin sums and interpolation analogues of sums of Vall\'{e}e Poussin from the functions that belong to the space $C_{\bar{\beta}}^\psi L_s, \ 1\leq s\leq\infty$…
The density of polynomials in a weighted space of infinitely differentiable functions in a multidimensional real space is proved under minimal conditions on weight functions and on differences between weight functions. We apply this result…
We obtain an estimate of the deviation of de la Vallee Poussin sums V_{n,n/2}(f;x) from continuous functions f, expressed in terms of values of theirs modulus of continuity. It is established that this estimate can't be improved by using…