Related papers: On the curved Trilinear Hilbert transform

An optimal control problem related to the probability of transition between stable states for a thermally driven Ginzburg-Landau equation is considered. The value function for the optimal control problem with a spatial discretization is…

We consider the scalar Helmholtz equation with variable, discontinuous coefficients, modelling transmission of acoustic waves through an anisotropic penetrable obstacle. We first prove a well-posedness result and a frequency-explicit bound…

We propose a method for solving constrained fixed point problems involving compositions of Lipschitz pseudo contractive and firmly nonexpansive operators in Hilbert spaces. Each iteration of the method uses separate evaluations of these…

We propose a new probabilistic numerical scheme for fully nonlinear equation of Hamilton-Jacobi-Bellman (HJB) type associated to stochastic control problem, which is based on the Feynman-Kac representation in [12] by means of control…

In this paper, we show that Hilbert transforms along some curves are bounded on $L^p({\mathbb R}^n;X)$ for some $1<p<\infty$ and some UMD spaces $X$. In particular, we prove that the Hilbert transform along some curves are completely…

In this paper, we propose a numerical method to approximate the solution of the time-dependent Schr\"odinger equation with periodic boundary condition in a high-dimensional setting. We discretize space by using the Fourier pseudo-spectral…

A classical approach for solving discrete time nonlinear control on a finite horizon consists in repeatedly minimizing linear quadratic approximations of the original problem around current candidate solutions. While widely popular in many…

This paper is concerned with a novel regularisation technique for solving linear ill-posed operator equations in Hilbert spaces from data that is corrupted by white noise. We combine convex penalty functionals with extreme-value statistics…

We consider Leray solutions of the three--dimensional incompressible Navier--Stokes equations on $\R^3$ with smooth, rapidly decaying initial data. The analysis is based on a frequency decomposition into low and high modes via the cutoffs…

Hamiltonian Monte Carlo (HMC) algorithms which combine numerical approximation of Hamiltonian dynamics on finite intervals with stochastic refreshment and Metropolis correction are popular sampling schemes, but it is known that they may…

We consider the efficient solution of strongly elliptic partial differential equations with random load based on the finite element method. The solution's two-point correlation can efficiently be approximated by means of an…

Self-excited limit-cycle oscillations (LCOs) from Hopf bifurcations are a key feature of nonlinear aeroelasticity and depend sensitively on structural and aerodynamic parameters. Classical center-manifold and normal-form theory describe…

In this paper we consider a mass- and energy--conserving Crank-Nicolson time discretization for a general class of nonlinear Schr\"odinger equations. This scheme, which enjoys popularity in the physics community due to its conservation…

This article is a study guide for "Trilinear smoothing inequalities and a variant of the triangular Hilbert transform" by Christ, Durcik, and Roos. We first present the standard techniques in the study of oscillatory integrals with the…

We consider models for multivariate point processes where the intensity is given nonparametrically in terms of functions in a reproducing kernel Hilbert space. The likelihood function involves a time integral and is consequently not given…

A commuting $n$-tuple $(T_1, \ldots, T_n)$ of bounded linear operators on a Hilbert space $\clh$ associate a Hilbert module $\mathcal{H}$ over $\mathbb{C}[z_1, \ldots, z_n]$ in the following sense: \[\mathbb{C}[z_1, \ldots, z_n] \times…

The purpose of this paper is to investigate several issues concerning the Dirac equation from a time-frequency analysis perspective. More precisely, we provide estimates in weighted modulation and Wiener amalgam spaces for the solutions of…

We make a complete variational treatment of rank-one Proper Generalised Decomposition for separable fractional partial differential equations with conformable derivatives. The setting is Hilbertian, the energy is induced by a symmetric…

We present supersymmetric, curved space, quantum mechanical models based on deformations of a parabolic subalgebra of osp(2p+2|Q). The dynamics are governed by a spinning particle action whose internal coordinates are Lorentz vectors…

In this article, using kernel convolution of order based dependent Dirichlet process (Griffin and Steel (2006)) we construct a nonstationary, nonseparable, nonparametric space-time process, which, as we show, satisfies desirable properties,…