arXiv subjects

Akitoshi Hoshiya

Publications and source records attributed to Akitoshi Hoshiya.

5 recordsLinked to original sources

arXiv2026

Dispersive estimates for Schr\"odinger operators with negative Coulomb-like potentials in one dimension

In this paper, we consider the dispersive estimates for Schr\"odinger operators with Coulomb-like decaying potentials, such as $V(x)=-c|x|^{-\mu}$ for $|x|\gg 1$ with $0<\mu<2$, in one dimension. As an application, we establish both the standard and orthonormal Strichartz estimates for this model. One of the difficulties here is that perturbation arguments, which are typically applicable to rapidly decaying potentials, are not available. To overcome this, we derive a WKB expression for the spectral density and use a variant of the degenerate stationary phase formula to exploit its oscillatory behavior in the low-energy regime.

math.AP↗

arXiv2025

Semiclassical limit of orthonormal Strichartz estimates on scattering manifolds

We study a quantum and classical correspondence related to the Strichartz estimates. First we consider the orthonormal Strichartz estimates on manifolds with ends. Under the nontrapping condition we prove the global-in-time estimates on manifolds with asymptotically conic ends or with asymptotically hyperbolic ends. Then we show that, for a class of pseudodifferential operators including the Laplace-Beltrami operator on the scattering manifolds, such estimates imply the global-in-time Strichartz estimates for the kinetic transport equations in the semiclassical limit. As a byproduct we prove that the existence of a periodic stable geodesic breaks the orthonormal Strichartz estimates. In the proof we do not need any quasimode. As an application we show the small data scattering for the cutoff Boltzmann equation on nontrapping scattering manifolds.

math.AP↗

arXiv2024

Uniform resolvent and orthonormal Strichartz estimates for repulsive Hamiltonian

We consider the uniform resolvent and orthonormal Strichartz estimates for the Schr\"odinger operator. First we prove the Keel-Tao type theorem for the orthonormal Strichartz estimates, which means that the dispersive estimates yield the orthonormal Strichartz estimates for strongly continuous unitary groups. This result applies to many Schr\"odinger propagators which are difficult to treat by the smooth perturbation theory, for example, local-in-time estimates for the Schr\"odinger operator with unbounded electromagnetic potentials, the $(k, a)$-generalized Laguerre operators and global-in-time estimates for the Schr\"odinger operator with scaling critical magnetic potentials including the Aharonov-Bohm potentials. Next we observe mapping properties of resolvents for the repulsive Hamiltonian and apply to the orthonormal Strichartz estimates. We prove the Kato-Yajima type uniform resolvent estimates with logarithmic decaying weight functions. This is new even when without perturbations. The proof is dependent on the microlocal analysis and the Mourre theory. We also discuss mapping properties on the Schwartz class and the Lebesgue space.

math.AP↗

arXiv2024

Orthonormal Strichartz estimate for dispersive equations with potentials

In this paper we prove the orthonormal Strichartz estimates for the higher order and fractional Schr\"odinger, wave, Klein-Gordon and Dirac equations with potentials. As in the case of the Schr\"odinger operator, the proofs are based on the smooth perturbation theory by T. Kato. However, for the Klein-Gordon and Dirac equations, we also use a method of the microlocal analysis in order to prove the estimates for wider range of admissible pairs. As applications we prove the global existence of a solution to the higher order or fractional Hartree equation with potentials which describes the dynamics of infinitely many particles. We also give a local existence result for the semi-relativistic Hartree equation with electromagnetic potentials. As another application, the refined Strichartz estimates are proved for higher order and fractional Schr\"odinger, wave and Klein-Gordon equations.

math.AP↗

arXiv2023

Orthonormal Strichartz estimates for Schr\"odinger operator and their applications to infinitely many particle systems

We develop an abstract perturbation theory for the orthonormal Strichartz estimates, which were first studied by Frank-Lewin-Lieb-Seiringer. The method used in the proof is based on the duality principle and the smooth perturbation theory by Kato. We also deduce the refined Strichartz estimates for the Schr\"odinger operator in terms of the Besov space. Finally we prove the global existence of a solution for the Hartree equation with electromagnetic potentials describing the dynamics of infinitely many fermions. This would be the first result on the orthonormal Strichartz estimates for the Schr\"odinger operator with general time-independent potentials including very short range and inverse square type potentials.

math-ph↗