Related papers: Discrete maximal operators over surfaces of higher…
This paper establishes optimal convergence rates for estimation of structured covariance operators of Gaussian processes. We study banded operators with kernels that decay rapidly off-the-diagonal and $L^q$-sparse operators with an…
This paper develops numerical methods for optimal control of mechanical systems in the Lagrangian setting. It extends the theory of discrete mechanics to enable the solutions of optimal control problems through the discretization of…
In this article, we set up the continuous maximal regularity theory for a class of linear differential operators on manifolds with singularities. These operators exhibit degenerate or singular behaviors while approaching the singular ends.…
We provide a representation of the $C^*$-algebra generated by multidimensional integral operators with piecewise constant kernels and discrete ergodic operators. This representation allows us to find the spectrum and to construct the…
Following the previous authors works (joint with I.A.Dynnikov) we develop a theory of the discrete analogs of the differential-geometrical (DG) connections in the triangulated manifolds. We study a nonstandard discretization based on the…
The behavior of certain weighted Hardy-type operators on rearrangement-invariant function spaces is thoroughly studied with emphasis being put on the optimality of the obtained results. First, the optimal rearrangement-invariant function…
Operator learning has been highly successful for continuous mappings between infinite-dimensional spaces, such as PDE solution operators. However, many operators of interest-including differential operators-are discontinuous or set-valued,…
A simple yet efficient computational algorithm for computing the continuous optimal experimental design for linear models is proposed. An alternative proof the monotonic convergence for $D$-optimal criterion on continuous design spaces are…
We study the boundedness of some sublinear operators on weighted Morrey spaces under certain size conditions. These conditions are satisfied by most of the operators in harmonic analysis, such as the Hardy-Littlewood maximal operator,…
In this paper, we study the spherical maximal operator $ M_E $ over $ E\subset [1,2]$, restricted to radial functions. In higher dimensions $ d\geq 3$, we establish a complete range of $ L^p-$improving estimates for $ M_E $. In two…
We consider a framework for the construction of iterative schemes for operator equations that combine low-rank approximation in tensor formats and adaptive approximation in a basis. Under fairly general assumptions, we obtain a rigorous…
For $2\leq p\leq \infty$, we establish dimension-free estimates for discrete dyadic Hardy-Littlewood maximal operators over Euclidean balls on semi-commutative $L_{p}$ space. In particular, when the radius is sufficiently large, these…
We study differential operators on an elliptic curve of order higher than 2 which are algebraically integrable (i.e., finite gap). We discuss classification of such operators of order 3 with one pole, discovering exotic operators on special…
Proximal operators are now ubiquitous in non-smooth optimization. Since their introduction in the seminal work of Moreau, many papers have shown their effectiveness on a wide variety of problems, culminating in their use to construct…
Despite the broad use of fixed-point iterations throughout applied mathematics, the optimal convergence rate of general fixed-point problems with nonexpansive nonlinear operators has not been established. This work presents an acceleration…
We construct in projective differential geometry of the real dimension $2$ higher symmetry algebra of the symplectic Dirac operator ${D}\kern-0.5em\raise0.22ex\hbox{/}_s$ acting on symplectic spinors. The higher symmetry differential…
The aim of the paper is firstly to study domains of definitions in terms of boundary conditions of minimal and maximal operators, as well as selfadjoint extensions of a minimal operator associated with the fourth-order differential operator…
We consider an elliptic optimal control problem where the objective functional contains an integral along a surface of codimension 1, also known as a hypersurface. In particular, we use a fidelity term that encourages the state to take…
This paper presents a mathematics-informed approach to neural operator design, building upon the theoretical framework established in our prior work. By integrating rigorous mathematical analysis with practical design strategies, we aim to…
In recent years, much effort in designing numerical methods for the simulation and optimization of mechanical systems has been put into schemes which are structure preserving. One particular class are variational integrators which are…