Related papers: On the invariance principle for a characteristic f…
Commuting integral and differential operators connect the topics of Signal Processing, Random Matrix Theory, and Integrable Systems. Previously, the construction of such pairs was based on direct calculation and concerned concrete special…
Given a function on diagonal matrices, there is a unique way to extend this to an invariant (by conjugation) function on symmetric matrices. We show that the extension preserves regularity -- that is, if the original function is k times…
Reparameterization invariance, a symmetry of heavy quark effective theory, appears in different forms in the literature. The most commonly cited forms of the reparameterization transformation are shown to induce the same constraints on…
We generalize the decomposition theorem for perverse sheaves to Artin stacks with affine stabilizers over finite fields.
We consider the elliptic differential operator defined as the sum of the minimum and the maximum eigenvalue of the Hessian matrix, which can be viewed as a degenerate elliptic Isaacs operator, in dimension larger than two. Despite of…
We consider generalized gradients in the general context of $G$-structures. They are natural first order differential operators acting on sections of vector bundles associated to irreducible $G$-representations. We study their geometric…
For oscillatory functions on local fields coming from motivic exponential functions, we show that integrability over $Q_p^n$ implies integrability over $F_p ((t))^n$ for large $p$, and vice versa. More generally, the integrability only…
In this note we study the application of generalized fractional operators to a particular class of nonstandard Lagrangians. These are typical of dissipative systems and the corresponding Euler-Lagrange and Hamilton equations are analyzed.…
We present a generalization of the inverse mapping theorem, where variations of a weaker non-expansiveness property (referred to as property ${\sf A}$) replace the key $\mathsf{C}^1$ condition. We also obtain inverse mapping theorems that…
We give sufficient Gordin-type criteria for the iterated (enhanced) weak invariance principle to hold for deterministic dynamical systems. Such an invariance principle is intrinsically related to the interpretation of stochastic integrals.…
The characteristic variety plays an important role in the analysis of the solution space of partial differential equations and exterior differential systems. This article studies the linear span of this variety, measuring its dimension via…
We present a novel approach of discretizing variable coefficient diffusion operators in the context of meshfree generalized finite difference methods. Our ansatz uses properties of derived operators and combines the discrete Laplace…
In this work we study the asymptotic behavior of solutions for a general linear second-order evolution differential equation in time with fractional Laplace operators in $\mathbb{R}^n$. We obtain improved decay estimates with less demand on…
We discuss some surprising phenomena from basic calculus related to oscillating functions and to the theorem on the differentiability of inverse functions. Among other things, we see that a continuously differentiable function with a strict…
A result by Courr\`ege says that linear translation invariant operators satisfy the maximum principle if and only if they are of the form $\mathcal{L}=\mathcal{L}^{\sigma,b}+\mathcal{L}^\mu$ where $$…
We present a construction of a large class of Laplace invariants for linear hyperbolic partial differential operators of fairly general form and arbitrary order.
In this note functions that transform open segments of a linear space into open segments of another linear space are studied and characterized. Assuming that the range is non-collinear, it is proved that such a map can always be expressed…
We prove a fiberwise almost sure invariance principle for random piecewise expanding transformations in one and higher dimensions using recent developments on martingale techniques.
For a very general class of unbounded self-adjoint operator function we prove upper bounds for eigenvalues which lie within arbitrary gaps of the essential spectrum. These upper bounds are given by triple variations. Furthermore, we find…
In this paper, we introduce the notion of a characteristic operator for closable linear operators and explore their connected spectral properties via equivalence. Additionally, we develop an explicit scheme for constructing characteristic…