Related papers: Redheffer representations and relaxed commutant li…
This paper studies the combinatoric structure of the set of all representations, up to equivalence, of a finite-dimensional semisimple Lie algebra. This has intrinsic interest as a previously unsolved problem in representation theory, and…
We give an extension to a nonconvex setting of the classical radial representation result for lower semicontinuous envelope of a convex function on the boundary of its effective domain. We introduce the concept of radial uniform upper…
The Koopman operator lifts nonlinear dynamical systems into a functional space of observables, where the dynamics are linear. In this paper, we provide three different Koopman representations for hybrid systems. The first is specific to…
Recently, we have proposed a new diffusive representation for fractional derivatives and, based on this representation, suggested an algorithm for their numerical computation. From the construction of the algorithm, it is immediately…
A major open problem in the Theory of Toeplitz operators on the analytic Bergman space over the unit disk is the characterization of the commutant of a given Toeplitz operator--that is, the set of all bounded Toeplitz operators that commute…
A major open question in the theory of Toeplitz operator on the Bergman space of the unit disk of the complex plane is to fully characterize the set of all Toeplitz operators that commute with a given one. In [2], the second author…
In this paper, we give a multiplication operator representation of bounded self-adjoint operators T on a Hilbert space H such that -- is a frame for H, for some -- . We state a necessary condition in order for a frame -- to have a…
A representation theorem for non-semibounded Hermitian quadratic forms in terms of a (non-semibounded) self-adjoint operator is proven. The main assumptions are closability of the Hermitian quadratic form, the direct integral structure of…
An $\left( n+1\right) -$D coefficient inverse problem for the radiative stationary transport equation is considered for the first time. A globally convergent so-called convexification numerical \ method is developed and its convergence…
Learning compatible representations enables the interchangeable use of semantic features as models are updated over time. This is particularly relevant in search and retrieval systems where it is crucial to avoid reprocessing of the gallery…
Leibniz' combinatorial formula for determinants is modified to establish a condensed and easily handled compact representation for Hessenbergians, referred to here as Leibnizian representation. Alongside, the elements of a fundamental…
We consider the canonical fundamental systems of solutions of linear homogeneous Caputo fractional differential equations with continuous variable coefficients. Here we gained a series-representation of the canonical fundamental system by…
We consider a single component reaction-diffusion equation in one dimension with bistable nonlinearity and a nonlocal space-fractional diffusion operator of Riesz-Feller type. Our main result shows the existence, uniqueness (up to…
We give a short survey on computational techniques which can be used to solve the representation conversion problem for polyhedra up to symmetries. We in particular discuss decomposition methods, which reduce the problem to a number of…
We use the methods of commutator and fundamental solutions to establish averaging lemmas and hypoelliptic estimates for purely kinetic transport equations. Assuming certain amount of velocity regularity for solutions, we extend our analysis…
For linear operators which factor with suitable assumptions concerning commutativity of the factors, we introduce several notions of a decomposition. When any of these hold then questions of null space and range are subordinated to the same…
We are interested in the numerical solution of nonsymmetric linear systems arising from the discretization of convection-diffusion partial differential equations with separable coefficients and dominant convection. Preconditioners based on…
We describe the numerical scheme for the discretization and solution of 2D elliptic equations with strongly varying piecewise constant coefficients arising in the stochastic homogenization of multiscale composite materials. An efficient…
Solutions of bilevel optimization problems tend to suffer from instability under changes to problem data. In the optimistic setting, we construct a lifted formulation that exhibits desirable stability properties under mild assumptions that…
The recently introduced weakly disentangled representations proposed to relax some constraints of the previous definitions of disentanglement, in exchange for more flexibility. However, at the moment, weak disentanglement can only be…