 Kenichi ITO |
Kenichi ITO
Department of Mathematics,
Graduate School of Science, Kobe University |
Division : Analysis
Professor |
Building B, Room 328

Personal Website
|
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), 673--709.
-
K. Ito and S. Nakamura,
Singularities of solutions to the Schrödinger equation on scattering
manifold, Amer. J. Math. 131 (2009), 1835-1865.
-
K. Ito and S. Nakamura,
Time-dependent scattering theory for Schrödinger operators on scattering
manifolds,
J. Lond. Math. Soc. (2) 81 (2010), 774--792.
-
K. Ito and S. Nakamura,
Remarks on the fundamental solution to Schrödinger equation with
variable coefficients, Ann. Inst. Fourier (Grenoble) 62 (2012),1091--1121.
-
K. Ito and E. Skibsted,
Scattering theory for Riemannian Laplacians, J. Funct. Anal. 264 (2013), 1929--1974.
-
K. Ito and S. Nakamura,
Microlocal properties of scattering matrices for Schrödinger equations
on scattering manifolds, Anal. PDE 6 (2013), 257--286.
-
K. Ito and E. Skibsted,
Absence of embedded eigenvalues for Riemannian Laplacians, Adv. Math.
248 (2013), 945--962.
-
K. Ito and E. Skibsted,
Absence of positive eigenvalues for hard-core $N$-body systems,
Ann. Henri Poincaré 12 (2014), 2379--2408.
-
K. Ito and A. Jensen,
A complete classification of threshold properties for one-dimensional discrete
Schrödinger operators,
Rev. Math. Phys. 27 (2015), 1550002 (45 pages).
|
|
|