Related papers: Estimates of perturbation series for kernels
In this paper we show numerically that for nonlinear Schrodinger type systems the presence of nonlocal perturbations can lead to a beyond-all-orders instability of stable solutions of the local equation. For the specific case of the…
In each dimension n >= 2, we construct a class of nonnegative potentials that are homogeneous of order -sigma, chosen from the range 0 < sigma < 2, and for which the perturbed Schrodinger equation does not satisfy global in time Strichartz…
We develop a framework for function classes generated by parametric ridge kernels: one-dimensional kernels composed with affine projections and averaged over a parameter measure. The induced kernels are positive definite, and the resulting…
We propose simple nonparametric estimators for mediated and time-varying dose response curves based on kernel ridge regression. By embedding Pearl's mediation formula and Robins' g-formula with kernels, we allow treatments, mediators, and…
We compute exact expressions of the noise kernel, defined as the expectation value of the symmetrized connected stress energy bitensor, for conformally-invariant scalar fields with respect to the conformal vacuum, valid for an arbitrary…
Starting from degree N solutions of a time dependent Schroedinger-like equation for classical orthogonal polynomials, a linear matrix equation describing perturbations around the N zeros of the polynomial is derived. The matrix has…
We give a functional characterization of a class of quasi-invariant determinantal processes corresponding to projection kernels in terms of de Branges spaces of entire funcitons.
A quantum integrable system slightly perturbed away from integrability is typically expected to thermalize on timescales of order $\tau\sim \lambda^{-2}$, where $\lambda$ is the perturbation strength. We here study classes of perturbations…
In this article we prove a reducibility result for the linear Schr\"odinger equation on the sphere $\mathbb{S}^{n}$ with quasi-periodic in time perturbation. Our result includes the case of unbounded perturbation that we assume to be of…
Parameter estimation in a class of heteroscedastic time series models is investigated. The existence of conditional least-squares and conditional likelihood estimators is proved. Their consistency and their asymptotic normality are…
Herein, the theory of Bergman kernel is developed to the weighted case. A general form of weighted Bergman reproducing kernel is obtained, by which we can calculate concrete Bergman kernel functions for specific weights and domains.
We examine an application of the kernel-based interpolation to numerical solutions for Zakai equations in nonlinear filtering, and aim to prove its rigorous convergence. To this end, we find the class of kernels and the structure of…
We derive large time upper bounds for heat kernels on vector bundles of differential forms on a class of non-compact Riemannian manifolds under certain curvature conditions.
We derive the Teukolsky equation for perturbations of a Kerr spacetime when the spacetime metric is written in either ingoing or outgoing Kerr-Schild form. We also write explicit formulae for setting up the initial data for the Teukolsky…
This article deals with a variation of constants type inequality for semigroups acting consistently on a scale of Banach spaces. This inequality can be characterized by a corresponding (easy to verify) inequality for their generators. The…
We study the semiclassical behaviour of a two--dimensional nonintegrable system. In particular we analyze the question of quantum corrections to the semiclassical quantization obtaining up to the second order of perturbation theory an…
Bursts of images exhibit significant self-similarity across both time and space. This motivates a representation of the kernels as linear combinations of a small set of basis elements. To this end, we introduce a novel basis prediction…
Time-dependent spherically-symmetric perturbations of Schwarzschild black holes are studied within torsion bigravity, i.e., within generalized Einstein-Cartan theories where the dynamical torsion carries massive spin-2 excitation. We reduce…
We construct the fundamental solution of $\partial_t-\Delta_y- q(t,y)$, for functions $q$ with a certain integral space-time relative smallness, in particular for those satisfying a relative Kato condition. The resulting transition density…
In this paper we study reducibility of time quasiperiodic perturbations of the quantum harmonic or anharmonic oscillator in one space dimension. We modify known algorithms obtaining a reducibility result which allows to deal with…