TAIRA, Kouichi

Title
Associate Professor
Field
Microlocal analysis, Spectral theory, Schrödinger equations
Research interests
Spectral theory, Smoothing effects and global-in-time behavior for dispersive equations
Current research

My research focuses on the spectral theory of differential operators, as well as smoothing effects and the long-time behavior of solutions to Schrödinger equations, using techniques from microlocal and harmonic analysis. Schrödinger operators represent the energy of quantum mechanical systems, and microlocal analysis allows us to investigate their spectral properties through the correspondence between quantum and classical mechanics. I am particularly interested in the spectral properties of non-elliptic differential operators, such as the d'Alembertian on curved spacetimes. Recent years have seen interesting developments on this topic in representation theory, and applications to quantum field theory on curved spacetimes have also been suggested. Existing methods, however, often fail to apply, and developing new analytical tools is one of the aspects of this research that I find particularly rewarding.
I also study how gravitational fields and potentials affect the smoothing properties and long-time behavior of solutions to Schrödinger equations.
Selected publications
  1. (with S. Nakamura) Essential self-adjointness of real principal type operators, Ann. Henri Lebesgue. 4, (2021), 1035--1059.
  2. Limiting absorption principle and equivalence of Feynman propagators on asymptotically Minkowski spacetimes, Commun. Math. Phys. 388 (2021), 625-655.
  3. (with H. Tamori) Strichartz estimates for the (k,a)-generalized Laguerre operators, SIGMA 21 (2025), 014, 37 pages.
  4. Equivalence of classical and quantum completeness for real principal type operators on the circle, Trans. Amer. Math. Soc. 379 (2026), no. 7 , 4809--4841.
  5. (with A. Hoshiya) Modified wave operators are unbounded on L^p for p≠2, preprint (2026) arXiv:2609.29729.

Memberships, activities and

Awards

The Mathematical Society of Japan