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 :
  1. 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.
  2. K. Ito and S. Nakamura, Singularities of solutions to the Schrödinger equation on scattering manifold, Amer. J. Math. 131 (2009), 1835-1865.
  3. K. Ito and S. Nakamura, Time-dependent scattering theory for Schrödinger operators on scattering manifolds, J. Lond. Math. Soc. (2) 81 (2010), 774--792.
  4. K. Ito and S. Nakamura, Remarks on the fundamental solution to Schrödinger equation with variable coefficients, Ann. Inst. Fourier (Grenoble) 62 (2012),1091--1121.
  5. K. Ito and E. Skibsted, Scattering theory for Riemannian Laplacians, J. Funct. Anal. 264 (2013), 1929--1974.
  6. K. Ito and S. Nakamura, Microlocal properties of scattering matrices for Schrödinger equations on scattering manifolds, Anal. PDE 6 (2013), 257--286.
  7. K. Ito and E. Skibsted, Absence of embedded eigenvalues for Riemannian Laplacians, Adv. Math. 248 (2013), 945--962.
  8. K. Ito and E. Skibsted, Absence of positive eigenvalues for hard-core $N$-body systems, Ann. Henri Poincaré 12 (2014), 2379--2408.
  9. 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).