Related papers: Functions with bounded Hessian-Schatten variation:…
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…
Let $M$ denote the centered Hardy--Littlewood operator on $\mathbb{R}$. We prove that \[ {\rm Var} (Mf)\le {\rm Var} (f) - \frac12\big| |f(\infty)|-|f(-\infty)|\big| \] for piecewise constant functions $f$ with nonzero and zero values…
We use the formalism of the R{\'e}nyi entropies to establish the symmetry range of extremal functions in a family of subcriti-cal Caffarelli-Kohn-Nirenberg inequalities. By extremal functions we mean functions which realize the equality…
The piecewise-concave function may be used to approximate a wide range of other functions to arbitrary precision over a bounded set. In this short paper, this property is proven for three function classes: (a) the multivariate twice…
Variational representations of divergences and distances between high-dimensional probability distributions offer significant theoretical insights and practical advantages in numerous research areas. Recently, they have gained popularity in…
We prove weighted analytic regularity for the solution of the integral fractional Poisson problem on bounded intervals with analytic right-hand side. Based on this regularity result, we prove exponential convergence of the hp-FEM on…
In this paper we deal with infinite horizon optimal control problems. Basing on weak variations in an extremal problem in weighted function spaces we prove necessary conditions in form of the adjoint equation and a variational inequality.…
We prove that certain quotients of entire functions are characteristic functions. Under some conditions, the probability measure corresponding to a characteristic function of that type has a density which can be expressed as a generalized…
Motivated by conforming finite element methods for elliptic problems of second order, we analyze the approximation of the gradient of a target function by continuous piecewise polynomial functions over a simplicial mesh. The main result is…
This paper studies the differentiability of the value function of switched linear systems under arbitrary switching and controlled switching, referred to as worst-case and optimal value functions respectively. First, we show that the value…
It is known that backward iterations of independent copies of a contractive random Lipschitz function converge almost surely under mild assumptions. By a sieving (or thinning) procedure based on adding to the functions time and space…
Hessian recovery has been commonly used in mesh adaptation for obtaining the required magnitude and direction information of the solution error. Unfortunately, a recovered Hessian from a linear finite element approximation is nonconvergent…
The paper demonstrates the basic properties of the local fractional variation operators (termed fractal variation operators). The action of the operators is demonstrated for local characterization of Holderian functions. In particular, it…
We consider a mixed variational problem in real Hilbert spaces, defined on on the unbounded interval of time and governed by a history-dependent operator. We state the unique solvability of the problem, which follows from a general…
In the first part of this paper we establish, in terms of so called k-tangential sets, a kind of optimal estimate for the size and structure of the set of non-differentiability of Lipshitz functions with one-sided directional derivatives.…
The Bayesian methods for linear inverse problems is studied using hierarchical Gaussian models. The problems are considered with different discretizations, and we analyze the phenomena which appear when the discretization becomes finer. A…
The maximum (or minimum) generalized eigenvalue of symmetric positive semidefinite matrices that depend on optimization variables often appears as objective or constraint functions in structural topology optimization when we consider…
In this paper, we establish a class of Stein-Weiss type inequality with partial variable weight functions on the upper half space using a weighted Hardy type inequality. Overcoming the impact of weighted functions, the existence of extremal…
Kernel expansions are a topic of considerable interest in machine learning, also because of their relation to the so-called feature maps introduced in machine learning. Properties of the associated basis functions and weights (corresponding…
In this paper we contribute to the frequently studied question of how to decompose a continuous piecewise linear (CPWL) function into a difference of two convex CPWL functions. Every CPWL function has infinitely many such decompositions,…