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, Exponential growth and decay estimates for eigenfunctions with complex eigenvalues. arXiv:2607.04180.
  2. T. Fujii, K. Ito, Characterization of spacetime singularities for the Schrödinger equation by initial state. arXiv:2604.02982.
  3. K. Ito, T. Tagawa, Propagation of space-time singularities for perturbed harmonic oscillators. arXiv:2512.24582.
  4. S. Arita, K. Ito, Elementary commutator method for the Dirac equation with long-range perturbations. arXiv:2511.08209.
  5. K. Ito, T. Tagawa, Low energy resolvent estimates for slowly decaying attractive potentials. Lett. Math. Phys. 116 (2026), 91. (SharedIt, arXiv)
  6. K. Ito, E. Skibsted, Scattering theory for C2 long-range potentials. J. Spectr. Theory 15 (2025), no. 1, pp. 353–439. (Open Access, arXiv, an extension of unpublished preprint.)
  7. T. Adachi, K. Itakura, K. Ito, E. Skibsted, Stationary scattering theory for 1-body Stark operators. Pure Appl. Funct. Anal. 7 (2022), no. 3, 825–861. (arXiv)
  8. K. Ito, E. Skibsted, Stationary scattering theory for 1-body Stark operators, II. Ann. Henri Poincaré 23 (2022), 513–548. (arXiv)
  9. K. Ito, E. Skibsted, Stationary scattering theory on manifolds. Ann. Inst. Fourier (Grenoble) 71 (2021), no. 3, 1065–1119. (Open Access, arXiv, formerly titled "Stationary scattering theory on mainifolds, II".)
  10. K. Ito, A. Jensen, Hypergeometric expression for the resolvent of the discrete Laplacian in low dimensions. Integr. Equ. Oper. Theory 93, 32 (2021). (Open Access, arXiv)
  11. 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. (arXiv)
  12. K. Ito, E. Skibsted, Radiation condition bounds on manifolds with ends. J. Funct. Anal. 278 (2020), no. 9, 108449. (arXiv, formerly titled "Stationary scattering theory on mainifolds, I".)
  13. T. Adachi, K. Itakura, K. Ito, E. Skibsted, Spectral theory for 1-body Stark operators. J. Differential Equations. 268 (2020), no. 9, 5179–5206. (arXiv)
  14. K. Ito, E. Skibsted, Time-dependent scattering theory on manifolds. J. Funct. Anal. 277 (2019), no. 5, 1423–1468. (Open Access, arXiv)
  15. K. Ito, A. Jensen, Branching form of the resolvent at threshold for multi-dimensional discrete Laplacians. J. Funct. Anal. 277 (2019), no. 4, 965–993. (Open Access, arXiv)
  16. 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. (arXiv)
  17. 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, arXiv)
  18. K. Ito, E. Skibsted, Rellich's theorem and N-body Schrödinger operators. Rev. Math. Phys. 28 (2016), no. 5, 1650010, 12 pp. (Repository, arXiv)
  19. 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, arXiv)
  20. K. Ito, E. Skibsted, Absence of positive eigenvalues for hard-core N-body systems. Ann. Henri Poincaré 15 (2014), no. 12, 2379–2408. (arXiv)
  21. K. Ito, E. Skibsted, Absence of embedded eigenvalues for Riemannian Laplacians. Adv. Math. 248 (2013), 945–962. (Open Access, Repository, arXiv)
  22. K. Ito, S. Nakamura, Microlocal properties of scattering matrices for Schrödinger equations on scattering manifolds. Anal. PDE 6 (2013), no. 2, 257–286. (arXiv)
  23. K. Ito, E. Skibsted, Scattering theory for Riemannian Laplacians. J. Funct. Anal. 264 (2013), no. 8, 1929–1974. (Open Access, Repository, arXiv)
  24. 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. (arXiv)
  25. 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. (arXiv)
  26. K. Ito, S. Nakamura, Singularities of solutions to the Schrödinger equation on scattering manifold. Amer. J. Math. 131 (2009), no. 6, 1835–1865. (arXiv)
  27. 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.
  28. 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. (Open Access)
  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. (Open Access)
  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. (Journal Page)
  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. (Open Access)

Teaching

My teaching slides are available here.

Contact

E-mail: "my_surname"-ken@math.kobe-u.ac.jp (Replace "my_surname" by my surname.)
Department of Mathematics, Graduate School of Science, Kobe University, 1-1, Rokkodai, Nada-ku, Kobe 657-8501, Japan