Kouichi Taira

activity

20172026

most citedLimiting absorption principle and equivalence of Feynman propagators on asymptotically Minkowski spacetimes

12 citations · 56 across the 19 of their papers we have counts for

collaborators

21 papers

math.SP2026

Large eigenvalues of the Connes-Moscovici operator

Kouichi Taira, Max Willems, Michał Wrochna

We prove the logarithmic Weyl law predicted by Connes and Moscovici for large positive eigenvalues of the distinguished self-adjoint extension of the operator $P=-\partial_x(x^2-1)…

math.AP2026

Modified wave operators are unbounded on $L^{p}$ for $p \neq = 2$

Akitoshi Hoshiya, Kouichi Taira

We study the $L^{p}$ -boundedness of Isozaki--Kitada type modified wave operators associated with Schrödinger operators $P = - \partial_{x}^{2} + V$ in one dimension for potentials $V$ inclu…

math.AP2026

Dispersive estimates for Schrödinger operators with negative Coulomb-like potentials in one dimension

Akitoshi Hoshiya, Kouichi Taira

In this paper, we consider the dispersive estimates for Schrödinger operators with Coulomb-like decaying potentials, such as $V (x) = - c ∣ x ∣^{- μ}$ for $∣ x ∣ ≫ 1$ with $0 < μ < 2$ , in one d…

math.AP2025

A microlocal Cauchy problem through a crossing point of Hamiltonian flows

Kenta Higuchi, Vincent Louatron, Kouichi Taira

In this paper, we consider $2 \times 2$ matrix-valued pseudodifferential equations in which the two characteristic sets intersect with finite contact order. We show that the asympto…

math.AP2025

Dispersive estimates and optimality for Schrödinger equations on product cones

Kouichi Taira

In this paper, we study time decay estimates for the Schrödinger propagator on the product cone $(X, g)$ , where $X = C (ρ S^{n - 1}) = (0, \infty) \times ρ S^{n - 1}$ . We prove…

math.AP2024

Local time decay for fractional Schrödinger operators with slowly decaying potentials and a weaker Agmon type estimate in a classically forbidden region

Kouichi Taira

A local time decay estimate of fractional Schrödinger operators with slowly decaying positive potentials are studied. It is shown that its resolvent is smooth near zero and the tim…

math.AP2023★ 1 cited

Strichartz Estimates for the $(k, a)$ -Generalized Laguerre Operators

Kouichi Taira, Hiroyoshi Tamori

In this paper, we prove Strichartz estimates for the $(k, a)$ -generalized Laguerre operators $a^{- 1} (- ∣ x ∣^{2 - a} Δ_{k} + ∣ x ∣^{a})$ which were introduced by Ben Sa\"ıd-Kobayashi-Or…

math.AP2022

Smoothness of the fundamental solution of Schrödinger equations with mild trapping

Kouichi Taira

In this short note, smoothness of the fundamental solution of Schrödinger equations on a complete manifold is studied. It is shown that (1) the fundamental solution is smooth under…

math-ph2022★ 7 cited

Essential self-adjointness for the Klein-Gordon type operators on asymptotically static spacetime

Shu Nakamura, Kouichi Taira

Let $X = R \times M$ be the spacetime, where $M$ is a closed manifold equipped with a Riemannian metric $g$ , and we consider a symmetric Klein-Gordon type operator $P$ on $X$ …

math-ph2022★ 9 cited

A remark on the essential self-adjointness for Klein-Gordon type operators

Shu Nakamura, Kouichi Taira

Here we discuss a new simplified proof of the essential self-adjointness for formally self-adjoint differential operators of real principal type, previously proved by Vasy (2020) a…

math.AP2021★ 2 cited

A remark on Strichartz estimates for Schrödinger equations with slowly decaying potentials

Kouichi Taira

In this short note, we prove Strichartz estimates for Schrödinger operators with slowly decaying singular potentials in dimension two. This is a generalization of the recent result…

math-ph2021

Remarks on the geodesically completeness and the smoothing effect on asymptotically Minkowski spacetimes

Kouichi Taira

In this note, we study a geometric property of asymptotically Minkowski spacetimes and an analytic property of the Klein-Gordon operator. Precisely, our first main results show tha…

math-ph2020★ 12 cited

Limiting absorption principle and equivalence of Feynman propagators on asymptotically Minkowski spacetimes

Kouichi Taira

In this paper, we shall show that the limiting absorption principle for the wave operator on the asymptotically Minkowski spacetime. This problem was previously considered by [A. V…

math.SP2020

Uniform resolvent estimates for the discrete Schrödinger operator in dimension three

Kouichi Taira

In this note, we prove the uniform resolvent estimate of the discrete Schrödinger operator with dimension three. To do this, we show a Fourier decay of the surface measure on the F…

math.AP2020★ 4 cited

Equivalence of classical and quantum completeness for real principal type operators on the circle

Kouichi Taira

In this article, we prove that the completeness of the Hamilton flow and essential self-adjointness are equivalent for real principal type operators on the circle. Moreover, we stu…

math.AP2019★ 8 cited

Essential self-adjointness of real principal type operators

Shu Nakamura, Kouichi Taira

We study the essential self-adjointness for real principal type differential operators. Unlike the elliptic case, we need geometric conditions even for operators on the Euclidean s…

math-ph2019★ 1 cited

Some properties of threshold eigenstates and resonant states of discrete Schrödinger operators

Yuji Nomura, Kouichi Taira

In this note, we study some properties of threshold resonant states or threshold eigenfunctions for discrete Schrödinger operators. We mainly prove two theorems. First, we prove th…

math.AP2019★ 2 cited

Scattering theory for repulsive Schrödinger operators and applications to limit circle problem

Kouichi Taira

In this note, we study existence of the outgoing/incoming resolvents of repulsive Schrödinger operators which may not be essentially self-adjoint on the Schwartz space. Moreover, w…

math.AP2019★ 5 cited

Limiting absorption principle on $L^{p}$ -spaces and scattering theory

Kouichi Taira

In this paper, we study the mapping property form $L^{p}$ to $L^{q}$ of the resolvent of the Fourier multiplier operators and scattering theory of generalized Schrödinger operators. Th…

math-ph2018

Uniform bounds of discrete Birman-Schwinger operators

Yukihide Tadano, Kouichi Taira

In this note, uniform bounds of the Birman-Schwinger operators in the discrete setting are studied. For uniformly decaying potentials, we obtain the same bound as in the continuous…

math.AP2017★ 5 cited

Strichartz estimates for non-degenerate Schrödinger equations

Kouichi Taira

We consider Schrödinger equation with a non-degenerate metric on the Euclidean space. We study local in time Strichartz estimates for the Schrödinger equation without loss of deriv…

Large eigenvalues of the Connes-Moscovici operator

Modified wave operators are unbounded on Lp for p=2

Dispersive estimates for Schrödinger operators with negative Coulomb-like potentials in one dimension

A microlocal Cauchy problem through a crossing point of Hamiltonian flows

Dispersive estimates and optimality for Schrödinger equations on product cones

Local time decay for fractional Schrödinger operators with slowly decaying potentials and a weaker Agmon type estimate in a classically forbidden region

Strichartz Estimates for the (k,a)-Generalized Laguerre Operators

Smoothness of the fundamental solution of Schrödinger equations with mild trapping

Essential self-adjointness for the Klein-Gordon type operators on asymptotically static spacetime

A remark on the essential self-adjointness for Klein-Gordon type operators

A remark on Strichartz estimates for Schrödinger equations with slowly decaying potentials

Remarks on the geodesically completeness and the smoothing effect on asymptotically Minkowski spacetimes

Limiting absorption principle and equivalence of Feynman propagators on asymptotically Minkowski spacetimes

Uniform resolvent estimates for the discrete Schrödinger operator in dimension three

Equivalence of classical and quantum completeness for real principal type operators on the circle

Essential self-adjointness of real principal type operators

Some properties of threshold eigenstates and resonant states of discrete Schrödinger operators

Scattering theory for repulsive Schrödinger operators and applications to limit circle problem

Limiting absorption principle on Lp-spaces and scattering theory

Uniform bounds of discrete Birman-Schwinger operators

Strichartz estimates for non-degenerate Schrödinger equations

Modified wave operators are unbounded on $L^{p}$ for $p \neq = 2$

Strichartz Estimates for the $(k, a)$ -Generalized Laguerre Operators

Limiting absorption principle on $L^{p}$ -spaces and scattering theory