Related papers: Constructive Approximation in Mixed norm Spaces
The Kantorovich exponential sampling series at jump discontinuities of the bounded measurable signal f has been analysed. A representation lemma for the series is established and using this lemma certain approximation theorems for…
Sampling theory in spaces other than the space of band-limited functions has recently received considerable attention. This is in part because the band-limitedness assumption is not very realistic in many applications. In addition,…
The article examines Nikolskii and Besov spaces with norms defined using "$L_p$-averaged" mixed moduli of continuity of functions of appropriate orders, instead of mixed moduli of continuity of known orders for certain mixed derivative…
We study multivariate integration and approximation for functions belonging to a weighted reproducing kernel Hilbert space based on half-period cosine functions in the worst-case setting. The weights in the norm of the function space depend…
In this paper we analyze a greedy procedure to approximate a linear functional defined in a Reproducing Kernel Hilbert Space by nodal values. This procedure computes a quadrature rule which can be applied to general functionals, including…
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…
We obtain the exact values of some important approximative quantities (such as, the best approximation, the basis width, Kolmogorov's width and the best $n$-term approximation) of certain sets of images of the diagonal operators in the…
Recently, versions of neural networks with infinite-dimensional affine operators inside the computational units (``neural operator'' networks) have been applied to learn solutions to differential equations. To enable practical computations,…
Operator learning based on neural operators has emerged as a promising paradigm for the data-driven approximation of operators, mapping between infinite-dimensional Banach spaces. Despite significant empirical progress, our theoretical…
We investigate affine Berkovich spaces over maximally complete fields and prove that they may be approximated by simpler spaces when the only functions we need to evaluate are polynomials of bounded degree. We derive applications to…
In solving scientific, engineering or pure mathematical problems one is often faced with a need to approximate the function of a given class by the linear combination of a preferably small number of functions that are localised one way or…
The purpose of this article is to give a Chlodowsky type generalization of Szasz operators defined by means of the Sheffer type polynomials. We obtain convergence properties of our operators with the help of Korovkin's theorem and the order…
We analyse the convergence of sampling algorithms for functions in reproducing kernel Hilbert spaces (RKHS). To this end, we discuss approximation properties of kernel regression under minimalistic assumptions on both the kernel and the…
The aim of this paper is to present a survey of some recent results obtained in the study of spaces with asymmetric norm. The presentation follows the ideas from the theory of normed spaces (topology, continuous linear operators, continuous…
In weighted Orlicz type spaces ${\mathcal S}_{_{\scriptstyle \mathbf p,\,\mu}}$ with a variable summation exponent, the direct and inverse approximation theorems are proved in terms of best approximations of functions and moduli of…
Here we research the univariate quantitative approximation, ordinary and fractional, of Banach space valued continuous functions on a compact interval or all the real line by quasi-interpolation Banach space valued neural network operators.…
Several optimization schemes have been known for convex optimization problems. However, numerical algorithms for solving nonconvex optimization problems are still underdeveloped. A progress to go beyond convexity was made by considering the…
Inspired by regularization techniques in statistics and machine learning, we study complementary composite minimization in the stochastic setting. This problem corresponds to the minimization of the sum of a (weakly) smooth function endowed…
Functions of one or more variables are usually approximated with a basis: a complete, linearly-independent system of functions that spans a suitable function space. The topic of this paper is the numerical approximation of functions using…
In this paper, we investigate necessary and sufficient conditions on the boundedness of composition operators on the Orlicz-Morrey spaces. The results of boundedness include Lebesgue and generalized Morrey spaces as special cases. Further,…