Homepage of Kenichi Ito

Research

I am working on spectral and scattering theory for the linear Schrödinger equation, particularly, on non-compact manifolds and discrete spaces.

List of Publications

Journal Articles and Preprints

  1. K. Ito, E. Skibsted, Stationary scattering theory for 1-body Stark operators, II. To appear in Ann. Henri Poincaré. (Preprint 2020)
  2. T. Adachi, K. Itakura, K. Ito, E. Skibsted, Stationary scattering theory for 1-body Stark operators. To appear in Pure Appl. Funct. Anal. (Preprint 2019)
  3. K. Ito, E. Skibsted, Stationary scattering theory on manifolds. To appear in Ann. Inst. Fourier (Grenoble). (Preprint 2016, titled "Stationary scattering theory on mainifolds, II".)
  4. K. Ito, A. Jensen, Hypergeometric expression for the resolvent of the discrete Laplacian in low dimensions. Integr. Equ. Oper. Theory 93, 32 (2021). (Preprint 2020)
  5. T. Adachi, K. Itakura, K. Ito, E. Skibsted, New methods in spectral theory of N-body Schrödinger operators. Rev. Math. Phys. 33 (2021), no. 5, 2150015, 48pp. (Preprint 2018)
  6. K. Ito, E. Skibsted, Radiation condition bounds on manifolds with ends. J. Funct. Anal. 278 (2020), no. 9, 108449. (Preprint 2016, titled "Stationary scattering theory on mainifolds, I".)
  7. T. Adachi, K. Itakura, K. Ito, E. Skibsted, Spectral theory for 1-body Stark operators. J. Differential Equations. 268 (2020), no. 9, 5179–5206. (Preprint 2019)
  8. K. Ito, E. Skibsted, Time-dependent scattering theory on manifolds. J. Funct. Anal. 277 (2019), no. 5, 1423–1468. (Preprint 2019)
  9. K. Ito, A. Jensen, Branching form of the resolvent at threshold for ultra-hyperbolic operators and discrete Laplacians. J. Funct. Anal. 277 (2019), no. 4, 965–993. (Preprint 2016)
  10. K. Ito, A. Jensen, Resolvent expansions for the Schrödinger operator on a graph with infinite rays. J. Math. Anal. Appl. 464 (2018), no. 1, 616–661. (Preprint 2017)
  11. K. Ito, A. Jensen, Resolvent expansions for the Schrödinger operator on the discrete half-line. J. Math. Phys. 58 (2017), no. 5, 052101, 24 pp. (Repository, Preprint 2016)
  12. K. Ito, E. Skibsted, Rellich's theorem and N-body Schrödinger operators. Rev. Math. Phys. 28 (2016), no. 5, 1650010, 12 pp. (Repository, Preprint 2016)
  13. K. Ito, A. Jensen, A complete classification of threshold properties for one-dimensional discrete Schrödinger operators. Rev. Math. Phys. 27 (2015), no. 1, 1550002, 45 pp. (Repository, Preprint 2013)
  14. K. Ito, E. Skibsted, Absence of positive eigenvalues for hard-core N-body systems. Ann. Henri Poincaré 15 (2014), no. 12, 2379–2408. (Preprint 2012)
  15. K. Ito, E. Skibsted, Absence of embedded eigenvalues for Riemannian Laplacians. Adv. Math. 258 (2013), 945–962. (Repository, Preprint 2011)
  16. K. Ito, S. Nakamura, Microlocal properties of scattering matrices for Schrödinger equations on scattering manifolds. Anal. PDE 6 (2013), no. 2, 257–286. (Preprint 2011)
  17. K. Ito, E. Skibsted, Scattering theory for Riemannian Laplacians. J. Funct. Anal. 264 (2013), no. 8, 1929–1974. (Repository, Preprint 2011)
  18. K. Ito, S. Nakamura, Remarks on the fundamental solution to Schrödinger equation with variable coefficients. Ann. Inst. Fourier (Grenoble) 62 (2012), no. 3, 1091–1121. (Preprint 2009)
  19. K. Ito, S. Nakamura, Time-dependent scattering theory for Schrödinger operators on scattering manifolds. J. Lond. Math. Soc. (2) 81 (2010), no. 3, 774–792. (Preprint 2008)
  20. K. Ito, S. Nakamura, Singularities of solutions to the Schrödinger equation on scattering manifold. Amer. J. Math. 131 (2009), no. 6, 1835–1865. (Preprint 2007)
  21. T. Akahori, K. Ito, Multilinear eigenfunction estimates for the harmonic oscillator and the nonlinear Schrödinger equation with the harmonic potential. Ann. Henri Poincaré 10 (2009), no. 4, 673–709.
  22. K. Ito, Propagation of singularities for Schrödinger equations on the Euclidean space with a scattering metric. Comm. Partial Differential Equations 31 (2006), no. 10-12, 1735–1777.

Proceedings

  1. T. Adachi, K. Itakura, K. Ito, E. Skibsted, Commutator methods for N-body Schrödinger operators. Spectral Theory and Mathematical Physics, STMP 2018, Santiago, Chile
  2. K. Ito, E. Skibsted, Spectral theory on manifolds. Advanced Studies in Pure Mathematics related to MSJ-SI 2018.
  3. K. Ito, A. Jensen, Resolvent expansion for the discrete one-dimensional Schrödinger operator. Mathematical results in quantum mechanics, 253–257, World Sci. Publ., Hackensack, NJ, 2015.
  4. K. Ito, E. Skibsted, Absence of embedded eigenvalues for the Schrödinger operator on manifold. Spectral and scattering theory and related topics, 69–75, RIMS Kôkyûroku Bessatsu, B45, Res. Inst. Math. Sci. (RIMS), Kyoto, 2014.
  5. K. Ito, E. Skibsted, Absence of positive eigenvalues for hard-core N-body systems. XVIIth International Congress on Mathematical Physics, 520–527, World Sci. Publ., Hackensack, NJ, 2014.
  6. K. Ito, S. Nakamura, Schrödinger equations on scattering manifolds and microlocal singularities. Spectral and scattering theory and related topics, 91–100, RIMS Kôkyûroku Bessatsu, B16, Res. Inst. Math. Sci. (RIMS), Kyoto, 2010.

Teaching

My teaching slides are available here.
Graduate School of Mathematical Sciences, The University of Tokyo, 3-8-1 Komaba, Meguro-ku, Tokyo 153-8914, Japan