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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

 
Shu Nakamura, Alexander Pushnitski
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY   366(4) 1725-1747   2014年4月   [査読有り]
The object of study in this paper is the on-shell scattering matrix S(E) of the Schrodinger operator with the potential satisfying assumptions typical in the theory of shape resonances. We study the spectrum of S(E) in the semiclassical limit when...
Kazuki Horie, Shu Nakamura
PUBLICATIONS OF THE RESEARCH INSTITUTE FOR MATHEMATICAL SCIENCES   50(3) 477-496   2014年   [査読有り]
In a previous paper by the second author [11], we discussed a characterization of the microlocal singularities for solutions to Schrodinger equations with long range type perturbations, using solutions to a Hamilton-Jacobi equation. In this paper ...
Shu Nakamura
JOURNAL OF SPECTRAL THEORY   4(3) 613-619   2014年   [査読有り]
On this short note, we apply the Mourre theory of the limiting absorption with difference type conditions on the potential, instead of conditions on the derivatives. In order that we modify the definition of the conjugate operator, and we apply th...
Mahito Kohmoto, Tohru Koma, Shu Nakamura
ANNALES HENRI POINCARE   14(5) 1413-1424   2013年7月   [査読有り]
We study the relationship between the spectral shift function and the excess charge in potential scattering theory. Although these quantities are closely related to each other, they have been often formulated in different settings so far. Here, we...
Kenichi Ito, Shu Nakamura
ANALYSIS & PDE   6(2) 257-286   2013年   [査読有り]
Let M be a scattering manifold, i.e., a Riemannian manifold with an asymptotically conic structure, and let H be a Schrodinger operator on M. One can construct a natural time-dependent scattering theory for H with a suitable reference system, and ...

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...