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We study the recovery of multivariate functions from reproducing kernel Hilbert spaces in the uniform norm. Our main interest is to obtain preasymptotic estimates for the corresponding sampling numbers. We obtain results in terms of the decay of related singular numbers of the compact embedding into $L_2(D,varrho_D)$ multiplied with the supremum of the Christoffel function of the subspace spanned by the first $m$ singular functions. Here the measure $varrho_D$ is at our disposal. As an application we obtain near optimal upper bounds for the sampling numbers for periodic Sobolev type spaces with general smoothness weight. Those can be bounded in terms of the corresponding benchmark approximation number in the uniform norm, which allows for preasymptotic bounds. By applying a recently introduced sub-sampling technique related to Weavers conjecture we mostly lose a $sqrt{log n}$ and sometimes even less. Finally we point out a relation to the corresponding Kolmogorov numbers.
In this paper we study $L_2$-norm sampling discretization and sampling recovery of complex-valued functions in RKHS on $D subset R^d$ based on random function samples. We only assume the finite trace of the kernel (Hilbert-Schmidt embedding into $L_2
In this paper we present results on asymptotic characteristics of multivariate function classes in the uniform norm. Our main interest is the approximation of functions with mixed smoothness parameter not larger than $1/2$. Our focus will be on the b
We consider the problem of reconstructing an unknown function $uin L^2(D,mu)$ from its evaluations at given sampling points $x^1,dots,x^min D$, where $Dsubset mathbb R^d$ is a general domain and $mu$ a probability measure. The approximation is picked
We tensorize the Faber spline system from [14] to prove sequence space isomorphisms for multivariate function spaces with higher mixed regularity. The respective basis coefficients are local linear combinations of discrete function values similar as
In this paper, we consider the minimization of a Tikhonov functional with an $ell_1$ penalty for solving linear inverse problems with sparsity constraints. One of the many approaches used to solve this problem uses the Nemskii operator to transform t