COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS 35(12) 2279-2309 2010年 [査読有り]
This paper is a continuation of [9], where short range perturbations of the flat Euclidian metric where considered. Here, we generalize the results of [9] to long-range perturbations (in particular, we can allow potentials growing like < x >...
AMERICAN JOURNAL OF MATHEMATICS 131(6) 1835-1865 2009年12月 [査読有り]
In this paper we study microlocal singularities of solutions to Schrodinger equations on scattering manifolds, i.e.. noncompact Riemannian manifolds with asymptotically conic ends. We characterize the wave front set of the solutions in terms of th...
ADVANCES IN MATHEMATICS 222(4) 1277-1307 2009年11月 [査読有り]
This paper is a continuation of [A. Martinez, S. Nakamura, V. Sordoni, Analytic smoothing effect for the Schrodinger equation with long-range perturbation, Comm. Pure Appl. Math. LIX (2006) 1330-1351], where an analytic smoothing effect was proved...
COMMUNICATIONS IN MATHEMATICAL PHYSICS 287(3) 1133-1143 2009年5月 [査読有り]
In the present note, we determine the ground state energy and study the existence of Lifshitz tails near this energy for some non monotonous alloy type models. Here, non monotonous means that the single site potential coming into the alloy random ...
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))....
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...
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