JOURNAL OF FUNCTIONAL ANALYSIS 256(4) 1299-1309 2009年2月 [査読有り]
We consider solutions to Schrodinger equation on R(d) with variable coefficients. Let H be the Schrodinger operator and let u(t) = e(-itH)u(0) be the solution to the Schrodinger equation with the initial condition u(0) is an element of L(2)(R(d))....
COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS 34(5) 506-519 2009年 [査読有り]
We consider Schrodinger equations with variable coefficients and the harmonic potential. We suppose the perturbation is short-range type in the sense of [7]. We characterize the wave front set of the solutions to the equation in terms of the class...
JOURNAL OF THE MATHEMATICAL SOCIETY OF JAPAN 61(1) 177-211 2009年1月 [査読有り]
We consider Schrodinger equations with variable coefficients, which are long-range type perturbations of the flat Laplacian on R-n. We characterize the wave front set of solutions to Schrodinger equations in terms of the initial state. Then it is ...
We consider the Schrodinger equation associated to long range perturbations of the flat Euclidean metric (in particular, potentials growing subquadratically at infinity are allowed). We construct a modified quantum free evolution G(0)(s) acting on...
COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS 59(9) 1330-1351 2006年9月 [査読有り]
We study the microlocal analytic singularity of solutions to the Schrodinger equation with analytic coefficients. Using microlocal weight estimates developed for estimating phase space tunneling, we prove microlocal smoothing estimates that genera...
Let be the spacetime, where is a closed manifold
equipped with a Riemannian metric , and we consider a symmetric Klein-Gordon
type operator on , which is asymptotically converges to a...
Here we discuss a new simplified proof of the essential self-adjointness for
formally self-adjoint differential operators of real principal type, previously
proved by Vasy (2020) and Nakamura-Taira (2021). For simplicity, here we
discuss the secon...
We consider the quantum graph Hamiltonian on the square lattice in Euclidean
space, and we show that the spectrum of the Hamiltonian converges to the
corresponding Schrödinger operator on the Euclidean space in the continuum
limit, and that the ...
We propose a method of data quantization of finite discrete-time signals
which optimizes the error estimate of low frequency Haar coefficients. We also
discuss the error/noise bounds of this quantization in the Fourier space. Our
result shows one ...
We consider scattering matrix for Schr\"odinger-type operators on with<br />
perturbation as . We show that<br />
the scattering matrix (with time-independent modifiers) is a pseudodifferent...
人文科学研究科
理学部