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In this paper we give an estimate for the solution to the Schr\"odinger equation with sub-quadratic potentials in modulation spaces by the norm of the initial functions in Wiener-Amalgum spaces.

We study non-smoothness of the fundamental solution for the Schr\"{o}dinger equation with a spherically symmetric and super-quadratic potential in the sence that $V(x)\geq C|x|^{2+\varepsilon}$ at infinity with constants $C>0 $ and $\varepsilon>0$. More precisely, we show the fundamental solution $E(t,x,y)$ does not belong to $C^{1}$ as a function of $(t,x,y)$., Comment: 18 pages

In this paper, we give estimates of the solutions to Schr\"{o}dinger equation on modulation spaces with vector potential of sub-linear growth.

We investigate the time propagation of singularity of a solution to linearized KdV equation by using the characterization of wave front sets with using to the wave packet transform (short time Fourier transform).

In this paper, we determine the C-infinity type wave front sets of the solutions to the Schrodinger equations with time-dependent variable coefficients and potentials by using the wave packet transform. We introduce the infinite sum and estimate the perturb terms of the flat Laplacian on flat plane, which cannot be estimated by the method in Kato-Ito., Comment: 12 pages

In this paper, we determine the wave front sets of solutions to Schr\"odinger equations of a harmonic oscillator with sub-quadratic perturbation by using the representation of the Schr\"odinger evolution operator of a harmonic oscillator via the wave packet transform.

In the present paper we obtain estimates in the modulation spaces for the solutions to the Dirac equation with quadratic and sub-quadratic potentials. We derive a representation for the Dirac operator that permits to solve approximately the perturbed Dirac equation and to obtain the desired estimates for the solution.

In this paper, we give a characterization of the ranges of the wave operators for Schrodinger equations with time-dependent short-range potentials by using wave packet transform. We also give an alternative proof of the existence of the wave operators for time-dependent potentials and the asymptotic completeness for timeindependent potentials., Comment: This article contains the results of "Scattering theory for Schrodinger equations with time-dependent short-range potentials via wave packet transform"(arXiv:1502.07170)

In this paper, we consider the existence and the asymptotic completeness of the wave operators for Schrodinger equations with time-dependent potentials which are short-range in space.

In this article, we determine the wave front sets of solutions to time dependent Schr\"odinger equations with a sub-quadratic potential by using the representation of the Schr\"dingier evolution operator via wave packet transform (short time Fourier transform)., Comment: 12 pages

In this paper, we give characterizations of usual wave front set and Sobolev type wave front set in terms of wave packet transform without any restriction on basic wave packet.

In this paper we give new estimates for the solution to the Schr\"odinger equation with quadratic and sub-quadratic potentials in the framework of modulation spaces.