Related papers: Some optimal recovery problems for operators on cl…
We prove an analogue of the Korneichuk--Stechkin lemma for functions with values in $L$-spaces. As applications, we obtain sharp Ostrowski type inequalities and solve problems of optimal recovery of identity and convexifying operators, as…
In this paper we consider the problem of optimization of approximate integration of set-valued functions from the class defined by given majorant of their moduli of continuity, using values of the functions at $n$ fixed or free points of…
The paper concerns problems of the recovery of linear operators defined on sets of functions from information of these functions given with stochastic errors. The constructed optimal recovery methods, in general, do not use all the…
In this paper we consider two recovery problems based on information given with an error. First is the problem of optimal recovery of the class $W^T_q = \{(t_1h_1,t_2h_2,\ldots)\in \ell_q\,:\,\|h\|_q\leqslant 1\}$, where $1\le q < \infty$…
Given pointwise samples of an unknown function belonging to a certain model set, one seeks in Optimal Recovery to recover this function in a way that minimizes the worst-case error of the recovery procedure. While it is often known that…
We give a systematic study on the Hardy spaces of functions with values in the non-commutative $L^p$-spaces associated with a semifinite von Neumann algebra ${\cal}M.$ This is motivated by the works on matrix valued Harmonic Analysis…
Optimal approximation and optimal interpolation problems on the classes of periodic functions that are determined by restrictions on several higher derivatives of the functions are solved.
{We explore a simple {\it geometric model} for functions between spaces of the same dimension (in infinite dimensions, we require that Jacobians be Fredholm operators of index zero). The model combines standard results in analysis and…
Function values are, in some sense, "almost as good" as general linear information for $L_2$-approximation (optimal recovery, data assimilation) of functions from a reproducing kernel Hilbert space. This was recently proved by new upper…
We find asymptotically optimal methods of recovery of the integration operator given values of the function at a finite number of points for a class of multivariate functions defined on a bounded star domain that have bounded in $L_p$ norm…
We study the recovery of functions in various norms, including $L_p$ with $1\le p\le\infty$, based on function evaluations. We obtain worst case error bounds for general classes of functions in terms of the best $L_2$-approximation from a…
We introduce a general framework for the reconstruction of periodic multivariate functions from finitely many and possibly noisy linear measurements. The reconstruction task is formulated as a penalized convex optimization problem, taking…
In this paper we introduce and study semigroups of operators on spaces of fuzzy-number-valued functions, and various applications to fuzzy differential equations are presented. Starting from the space of fuzzy numbers, many new spaces…
The problems of optimal recovery of unbounded operators are studied. Optimality means the highest possible accuracy and the minimal amount of discrete information involved. It is established that the truncation method, when certain…
We deal with the boundedness of the multilinear fractional integral operator $I_{\gamma,m}$ from a product of weighted Lebesgue spaces into adequate weighted Lipschitz spaces. Our results generalize some previous estimates not only for the…
The paper concerns problems of the recovery of differential operators from a noisy Fourier transform. In particular, optimal methods are obtained for the recovery of powers of generalized Laplace operators from a noisy Fourier transform in…
We study the optimal recovery problem for isotropic functions defined by second-order differential operators using both function and gradient values. We derive the upper bound for n-th optimal error with an explicit constant, which is…
We present an approach for variational regularization of inverse and imaging problems for recovering functions with values in a set of vectors. We introduce regularization functionals, which are derivative-free double integrals of such…
Much recent work has addressed the solution of a family of partial differential equations by computing the inverse operator map between the input and solution space. Toward this end, we incorporate function-valued reproducing kernel Hilbert…
We consider the problem of optimal recovery of an element $u$ of a Hilbert space $\mathcal{H}$ from $m$ measurements obtained through known linear functionals on $\mathcal{H}$. Problems of this type are well studied \cite{MRW} under an…