Related papers: On Two Methods for Quantitative Unique Continuatio…
Motivated by a growing list of nontraditional statistical estimation problems of the piecewise kind, this paper provides a survey of known results supplemented with new results for the class of piecewise linear-quadratic programs. These are…
We consider the weighted eigenvalue problem for a general non-local pseudo-differential operator, depending on a bounded weight function. For such problem, we prove that strict (decreasing) monotonicity of the eigenvalues with respect to…
In this work, we present a systematic approach to investigate the existence, multiplicity, and local gradient regularity of solutions for nonlocal quasilinear equations with local gradient degeneracy. Our method involves an interactive…
In this note we reprove the Lipschitz stability for the inverse problem for the Schr\"odinger operator with finite-dimensional potentials by using quantitative Runge approximation results. This provides a quantification of the Schr\"odinger…
We extend the maximal unitarity method at two loops to double-box basis integrals with up to three external massive legs. We use consistency equations based on the requirement that integrals of total derivatives vanish. We obtain unique…
To entirely determine the resulting functions of one-loop integrals it is necessary to find the correct analytic continuation to all relevant kinematical regions. We argue that this continuation procedure may be performed in a general and…
We introduce compactness classes of Hilbert space operators by grouping together all operators for which the associated singular values decay at a certain speed and establish upper bounds for the norm of the resolvent of operators belonging…
We consider the Cauchy problem for the logarithmic Schr\"odinger equation and prove uniqueness of weak $H^s(\mathbb{R}^d)$ solutions for $s\in(0,1)$, which improves on the previous uniqueness result in $H^1(\mathbb{R}^d)$. The proof is…
In numerical approaches to solving differential equations on a lattice, a representation of the derivative operator that correctly matches the continuum behaviour of functions of momentum up to the band limit must be non-local. We present…
Finite-sum optimization has wide applications in machine learning, covering important problems such as support vector machines, regression, etc. In this paper, we initiate the study of solving finite-sum optimization problems by quantum…
We prove the validity of regularizing properties of a double layer potential associated to the fundamental solution of a {\em nonhomogeneous} second order elliptic differential operator with constant coefficients in Schauder spaces by…
We obtain a unique continuation result at infinity for fully nonlinear elliptic integro-differential operators of order 2s which satisfy the maximum and minimum principles in bounded subdomains, under the decay assumption $o(|x|^{-(N+2s)})$…
Consider the following distributed optimization scenario. A worker has access to training data that it uses to compute the gradients while a server decides when to stop iterative computation based on its target accuracy or delay…
A leading twist expansion in terms of bi-local operators is proposed for the structure functions of deeply inelastic scattering near the elastic limit $x \to 1$, which is also applicable to a range of other processes. Operators of…
We investigate low-regularity integrator (LRI) methods for the Q-tensor model governing nematic liquid-crystalline semilinear parabolic equation. First- and second-order temporal discretizations are developed using Duhamel's formula, and we…
We obtain a probabilistic proof of the local Lipschitz continuity for the optimal stopping boundary of a class of problems with state space $[0,T]\times\mathbb{R}^d$, $d\ge 1$. To the best of our knowledge this is the only existing proof…
This paper addresses the challenging numerical simulation of nonlinear hybrid stochastic functional differential equations with infinite delays. We first propose an explicit scheme using space and time truncation, requiring only finite…
In this paper we study unique continuation theorems for magnetic Schr\"odinger equation via Carleman estimates. We use integration by parts techniques in order to show these estimates. We consider electric and magnetic potentials with…
We derive a dynamical bound on the propagation of correlations in local random quantum circuits - lattice spin systems where piecewise quantum operations - in space and time - occur with classical probabilities. Correlations are quantified…
In this paper, we first prove some local estimates for bilinear operators (closely related to the bilinear Hilbert transform and similar singular operators) with truncated symbol. Such estimates, in accordance with the Heisenberg…