Related papers: Local dispersive and Strichartz estimates for the …
This paper is dedicated to the proof of Strichartz estimates on the Heisenberg group $\mathbb{H}^d$ for the linear Schr\"odinger and wave equations involving the sublaplacian. The Schr\"odinger equation on $\mathbb{H}^d$ is an example of a…
In this paper we study the linear and nonlinear Schr\"odinger equations associated with the Ornstein-Uhlenbeck (OU) operator endowed with the Gaussian measure. While classical Strichartz estimates are well-developed for the free…
This paper aims to give a general (possibly compact or noncompact) analog of Strichartz inequalities with loss of derivatives, obtained by Burq, G\'erard, and Tzvetkov [19] and Staffilani and Tataru [51]. Moreover we present a new approach,…
The aim of this article is to give the well-posedness results for the Cauchy problem of the nonlinear Schr\"odinger equation with power type nonlinearities on H-type groups. To do this, we prove the dispersive estimate and Strichartz…
We prove dispersive and Strichartz estimates for Schr\"o- dinger equations on a class of locally symmetric spaces {\Gamma}\X, where X = G/K is a symmetric space and {\Gamma} is a torsion free discrete sub- group of G. We deal with the cases…
We establish sharp-in-time kernel and dispersive estimates for the Schr\"odinger equation on non-compact Riemannian symmetric spaces of any rank. Due to the particular geometry at infinity and the Kunze-Stein phenomenon, these properties…
In this paper, we prove the dispersive estimates and Strichartz inequalities for the solution of the Schr\"{o}dinger equation related to the full Laplacian on H-type groups. This extends the results obtained by G. Furioli and A. Veneruso…
Let $G=-\Delta-|x|^2\partial_{t}^2$ denote the Grushin operator on $\mathbb{R}^{n+1}$. The aim of this paper is two fold. In the first part, due to the non-dispersive phenomena of the Grushin-Schr\"odinger equation on $\mathbb{R}^{n+1}$, we…
Let $\mathcal{L}$ be the sub-Laplacian on H-type groups and $\phi: \mathbb{R}^+ \to \mathbb{R}$ be a smooth function. The primary objective of the paper is to study the decay estimate for a class of dispersive semigroup given by…
We give the upper and the lower estimates of heat kernels for Schr\"odinger operators $H=-\Delta+V$, with nonnegative and locally bounded potentials $V$ in $\mathbb{R}^d$, $d \geq 1$. We observe a factorization: the contribution of the…
The nonlinear Schr\"odinger equation plays a fundamental role in mathematical physics, particularly in the study of quantum mechanics and Bose-Einstein condensation. This paper explores two distinct approaches to establishing the local…
Strichartz estimates are a manifestation of a dispersion phenomenon, exhibited by certain partial differential equations, which is detected by suitable Lebesgue space norms. In most cases the evolution propagator $U(t)$ is a one parameter…
We establish global bounds for solutions to stationary and time-dependent Schr\"odinger equations associated with the sublaplacian $\mathcal L$ on the Heisenberg group, as well as its pure fractional power $\mathcal L^s$ and conformally…
We prove dispersive and Strichartz estimates for Schr\"{o}dinger equations on normal real form symmetric spaces. These estimates apply to the well-posedness and scattering for the nonlinear Schr\"{o}dinger equations.
For a large class of complete, non-compact Riemannian manifolds, $(M,g)$, with boundary, we prove high energy resolvent estimates in the case where there is one trapped hyperbolic geodesic. As an application, we have the following local…
We prove Strichartz estimates for the Schr\"odinger equation with scaling-critical electromagnetic potentials in dimensions $n\geq3$. The decay assumption on the magnetic potentials is critical, including the case of the Coulomb potential.…
We prove a dispersive estimate for periodic discrete Schr\"odinger operators on the line with optimal rate of decay. Additionally, by standard methods, we deduce dispersive estimates for the discrete nonlinear Schr\"odinger equation with…
We study dispersive properties of the one-dimensional Schr{\"o}dinger equation with a short-range array of delta interactions. More precisely, we consider the self-adjoint operator obtained by perturbing the free Laplacian on the line with…
We prove some new Strichartz estimates for a class of dispersive equations with radial initial data. In particular, we obtain up to some endpoints the full radial Strichartz estimates for the Schr\"odinger equation. The ideas of proof are…
In this article we study global-in-time Strichartz estimates for the Schr\"odinger evolution corresponding to long-range perturbations of the Euclidean Laplacian. This is a natural continuation of a recent article of the third author, where…