Related papers: Analysis of Schr\"odinger means

Maximal estimates for Schr\"odinger means and convergence almost everywhere of sequences of Schr\"odinger means are studied.

New estimates on the maximal function associated to the linear Schrodinger equation are established

Localization properties for Schr\"odinger means are studied in dimension higher than one.

Multiparameter maximal estimates are considered for operators of Schr\"odinger type. Sharp and almost sharp results, that extend work by Rogers and Villarroya, are obtained. We provide new estimates via the integrability of the kernel which…

We give new lower bounds for $L^p$ estimates of the Schr\"odinger maximal function by generalizing an example of Bourgain.

We obtain $L^p$ estimates of the maximal Schr\"odinger operator in $\mathbb R^n$ using polynomial partitioning, bilinear refined Strichartz estimates, and weighted restriction estimates.

In this paper, we studied the space-time estimates for the solution to the Schr\"odinger equation. By polynomial partitioning, induction arguments, bilinear to linear arguments and broad norm estimates, we set up several maximal estimates…

We study convergence almost everywhere of sequences of Schr\"odinger means. We also replace sequences by uncountable sets.

In this paper we study sharp estimates for the Schr\"odinger operator via the framework of orthogonal polynomials. We use spherical harmonics and Gegenbauer polynomials to prove a new weighted inequality for the Schr\"odinger equation that…

This note presents a new proof of the well-known Strichartz estimates for the Schr\"odinger equation in $2+1$ dimensions, building on ideas from our recent work \cite{MO}.

For the one-dimensional Schr\"odinger equation, we obtain sharp maximal-in-time and maximal-in-space estimates for systems of orthonormal initial data. The maximal-in-time estimates generalize a classical result of Kenig--Ponce--Vega and…

We present some old and new results on dispersive estimates for Schroedinger equations.

In this work we prove a Strichartz estimate for the Schr\"odinger equation in the quasiperiodic setting. We also show a lower bound on the number of resonant frequency interactions in this situation.

Estimates for the total multiplicity of eigenvalues for Schr\"odinger operator are established in the case of compactly supported or exponentially decreasing complex-valued potential.

We prove (essentially) sharp $L^4$ level set estimates for the periodic Schr\"odinger maximal operator in a certain range of the cut-off parameter.

Almost everywhere convergence on the solution of Schr\"odinger equation is an important problem raised by Carleson in harmonic analysis. In recent years, this problem was essentially solved by building the sharp $L^p$-estimate of…

We study the one-dimensional Schr\"odinger equation and derive exact expressions for the Green function in terms of reflection coefficients which are defined for semi-infinite intervals. We also discuss the relation between our results and…

We obtain weighted mixed inequalities for operators associated to a critical radius function. We consider Schr\"odinger Calder\'on-Zygmund operators of $(s,\delta)$ type, for $1<s\leq \infty$ and $0<\delta \leq 1$. We also give estimates of…

We prove optimal high-frequency resolvent estimates for perturbations by large magnetic and electric potentials

Using Guth's polynomial partitioning method, we obtain $L^p$ estimates for the maximal function associated to the solution of Schr\"odinger equation in $\mathbb R^2$. The $L^p$ estimates can be used to recover the previous best known result…