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中村 周

 
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研究者氏名中村 周
 
ナカムラ シュウ
URLhttp://pc1.math.gakushuin.ac.jp/~shu/
所属学習院大学
部署理学部数学科
職名教授
学位理学博士(東京大学)
科研費研究者番号50183520

研究キーワード

 
超局所解析 , 半古典解析 , 散乱理論 , シュレディンガー方程式

研究分野

 
  • 自然科学一般 / 基礎解析学 / 関数解析、関数方程式

論文

 
Frederic Klopp, Shu Nakamura
ANALYSIS & PDE   3(4) 409-426   2010年   [査読有り]
We study Lifshitz tails for random Schrodinger operators where the random potential is alloy-type in the sense that the single site potentials are independent, identically distributed, but they may have various function forms. We suppose the singl...
Andre Martinez, Shu Nakamura, Vania Sordoni
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 >...
Kenichi Ito, Shu Nakamura
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...
Andre Martinez, Shu Nakamura, Vania Sordoni
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...
Frederic Klopp, Shu Nakamura
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 ...

MISC

 
Shu Nakamura
   2018年4月
We consider scattering matrix for Schr\&quot;odinger-type operators on Tex with<br />
perturbation Tex as Tex. We show that<br />
the scattering matrix (with time-independent modifiers) is a pseudodifferent...
Shu Nakamura
   2018年4月
We show that the scattering matrix for a class of Schr\&quot;odinger-type<br />
operators with long-range perturbations is a Fourier integral operator with the<br />
phase function which is the generating function of the modified classical<br />
s...
Jussi Behrndt, Fritz Gesztesy, Shu Nakamura
   2017年10月
For the pair Tex of self-adjoint<br />
Schr\&quot;{o}dinger operators in Tex a spectral shift function is<br />
determined in an explicit form with the help of (energy parameter dependent...
Jussi Behrndt, Fritz Gesztesy, Shu Nakamura
   2016年9月
The spectral shift function of a pair of self-adjoint operators is expressed<br />
via an abstract operator valued Titchmarsh--Weyl Tex-function. This general<br />
result is applied to different self-adjoint realizations of second-order<br />
ell...
Shu Nakamura
   2016年2月
Let Tex be a Schr\&quot;odinger type operator with long-range perturbation. We<br />
study the wave front set of the distribution kernel of Tex, where Tex is in the absolutely continous spectrumof Tex.The<br />
res...