Kenichi ITO 
Kenichi ITO
Department of Mathematics,
Graduate School of Science, Kobe University 
Division : Analysis
Associate Professor 
Building B, Room 322

Research Field :
Schrödinger equation, analysis on manifolds, microlocal analysis


Research Summary :
I am studying the Schröodinger equation on noncompact manifolds.
The research of the Schröodinger equation on the Euclidean space has a long history,
and lots of powerful tools and techniques have been developped
in order to treat a wide variety of perturbations.
I believe that such powerful theories should be applicable to more geometric problems too,
and would provide new methods or theories in the geometric analysis.


Primary Publications : 

T. Akahori and K. Ito,
Multilinear eigenfunction estimates for the harmonic oscillator and the
nonlinear Schrödinger equation with the harmonic potential, Ann. Henri
Poincaré 10 (2009), 673709.

K. Ito and S. Nakamura,
Singularities of solutions to the Schrödinger equation on scattering
manifold, Amer. J. Math. 131 (2009), 18351865.

K. Ito and S. Nakamura,
Timedependent scattering theory for Schrödinger operators on scattering
manifolds,
J. Lond. Math. Soc. (2) 81 (2010), 774792.

K. Ito and S. Nakamura,
Remarks on the fundamental solution to Schrödinger equation with
variable coefficients, Ann. Inst. Fourier (Grenoble) 62 (2012),10911121.

K. Ito and E. Skibsted,
Scattering theory for Riemannian Laplacians, J. Funct. Anal. 264 (2013), 19291974.

K. Ito and S. Nakamura,
Microlocal properties of scattering matrices for Schrödinger equations
on scattering manifolds, Anal. PDE 6 (2013), 257286.

K. Ito and E. Skibsted,
Absence of embedded eigenvalues for Riemannian Laplacians, Adv. Math.
248 (2013), 945962.

K. Ito and E. Skibsted,
Absence of positive eigenvalues for hardcore $N$body systems,
Ann. Henri Poincaré 12 (2014), 23792408.

K. Ito and A. Jensen,
A complete classification of threshold properties for onedimensional discrete
Schrödinger operators,
Rev. Math. Phys. 27 (2015), 1550002 (45 pages).


