arXiv subjects
Publications and source records attributed to Keiichi Kato.
We study the wave front set of the solutions of the initial value problem for nonlinear Schr\"{o}dinger equations via wave packet transform. We give an sufficient condition which assures that the solutions is in Sobolev space of order s in a given direction at a given time.
We study non-smoothness of the fundamental solution for the Schrödinger 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 $(t,x,y)$.
In this paper we give an estimate for the solution to the Schrödinger equation with sub-quadratic potentials in modulation spaces by the norm of the initial functions in Wiener-Amalgum spaces.
In this paper, we give estimates of the solutions to Schrödinger 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 wave front sets of solutions to Schrödinger equations of a harmonic oscillator with sub-quadratic perturbation by using the representation of the Schrödinger evolution operator of a harmonic oscillator via the wave packet 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.
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.
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 Schrödinger equations with a sub-quadratic potential by using the representation of the Schrdingier evolution operator via wave packet transform (short time Fourier transform).
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 Schrödinger equation with quadratic and sub-quadratic potentials in the framework of modulation spaces.