Related papers: Local linear dependence of linear partial differen…
Lower and upper bounds for a given function are important in many mathematical and engineering contexts, where they often serve as a base for both analysis and application. In this short paper, we derive piecewise linear and quadratic…
We give a necessary and sufficient condition for non-local functionals on vector-valued Lebesgue spaces to be weakly sequentially lower semi-continuous. Here a non-local functional shall have the form of a double integral of a density which…
We study a fractional differentiation operator for functions on the conjugate space to an infinite extension of a local field of zero characteristic which is a union of an increasing sequence of finite extensions. In particular, a…
We prove boundedness and regularity estimates for weak solutions to a class of linear nonlocal equations involving integro-differential operators with almost no order of differentiability. In particular, we show that bounded weak solutions…
Local solvability is analyzed for natural families of partial differential operators having double characteristics. In some families the set of all operators that are not locally solvable is shown to have both infinite dimension and…
In the present article, we discuss some aspects of the local stability analysis for a class of abstract functional differential equations. This is done under smoothness assumptions which are often satisfied in the presence of a…
In this article, we give a representation of bounded complex linear operators which preserve idempotent elements on the Fourier algebra of a locally compact group. When such an operator is moreover positive or contractive, we show that the…
We consider dynamical systems arising from substitutions over a finite alphabet. We prove that such a system is linearly repetitive if and only if it is minimal. Based on this characterization we extend various results from primitive…
If a linear differential operator with rational function coefficients is reducible, its factors may have coefficients with numerators and denominatorsof very high degree. When the base field is $\mathbb C$, we give a completely explicit…
We introduce a general difference quotient representation for non-local operators associated with a first-order linear operator. We establish new local to non-local estimates and strong localization principles in various spaces of…
In functional data analysis, functional linear regression has attracted significant attention recently. Herein, we consider the case where both the response and covariates are functions. There are two available approaches for addressing…
In this paper, we give conditions forcing nilpotent operators (everywhere bounded or closed) to be null. More precisely, it is mainly shown any closed or everywhere defined bounded nilpotent operator with a positive (self-adjoint) real part…
Given a differential operator defined in terms of left-invariant vector fields on a Lie group, we prove that the local condition defining maximal hypoellipticity is equivalent to a global estimate if the operator is left invariant. As a…
A continuous linear operator $T:E \to F$ is called strictly singular if it cannot be invertible on any infinite dimensional closed subspace of its domain. In this note we discuss sufficient conditions and consequences of the phenomenon…
We prove a tight lower bound (up to constant factors) on the sample complexity of any non-interactive local differentially private protocol for optimizing a linear function over the simplex. This lower bound also implies a tight lower bound…
We consider Delone sets with finite local complexity. We characterize validity of a subadditive ergodic theorem by uniform positivity of certain weights. The latter can be considered to be an averaged version of linear repetitivity. In this…
Extending a fundamental result for (indefinite) quadratic programs, this paper shows that certain non-convex piecewise programs have only a finite number of directional stationary values, and thus, possess only finitely many locally minimum…
We give a condition ensuring that the operators in a nilpotent Lie algebra of linear operators on a finite dimensional vector space have a common eigenvector.
A space X has the local fixed point property LFPP, (local periodic point property LPPP) if it has an open basis $\mathcal{B}$ such that, for each $B\in \mathcal{B}$, the closure $\overline{B}$ has the fixed (periodic) point property. Weaker…
A wide class of non-autonomous nonlinear parabolic partial differential equations with delay is studied. We allow in our investigations different types of delays such as constant, time-dependent, state-dependent (both discrete and…