arXiv subjects

Kotaro Inami

Publications and source records attributed to Kotaro Inami.

4 recordsLinked to original sources

arXiv2026

Strichartz estimates for quasi-periodic functions on long time intervals: An arithmetic approach

We study long-time Strichartz estimates for the one-dimensional Schr\"{o}dinger equation with quasi-periodic initial data. For two-frequency data with an algebraic frequency ratio, we observe that the behavior of the linear Schr\"{o}dinger evolution changes depending on the algebraic degree of the ratio. Making use of this observation, we improve the Strichartz estimates on long time intervals. We also prove an endpoint $L^4$ Strichartz estimate. Our proofs use Roth-type Diophantine inequalities and Vinogradov-type mean value estimates for the Parsell--Vinogradov systems.

math.AP↗

arXiv2026

Reverse square function estimates for degenerate curves and its applications

Building on the classical work of C\'{o}rdoba--Fefferman and the recent work of Schippa, we establish $L^4$ reverse square function estimates for functions whose Fourier support is contained in a $\delta$-neighborhood of the curve $\{(\xi,\xi^a): |\xi|\leq 1\}$ in $\mathbb{R}^2$, for all exponents $a\in(0,\infty)\backslash\{1\}$. As applications, we derive sharp $L^4$ Strichartz estimates on the one-dimensional torus for fractional Schr\"{o}dinger equations and establish new local smoothing estimates in modulation spaces. In the latter application, orthogonal Strichartz-type estimates also play a crucial role.

math.CA↗

arXiv2024

Local smoothing estimates for Schr\"odinger equations in modulation spaces

Motivated by a recent work of Schippa (2022), we consider local smoothing estimates for Schr\"{o}dinger equations in modulation spaces. By using the C\'{o}rdoba-Fefferman type reverse square function inequality and the bilinear Strichartz estimate, we can refine the summability exponent of modulation spaces. Next, we will also discuss a new type of randomized Strichartz estimate in modulation spaces. Finally, we will show that the reverse function estimate implies the Strichartz estimates in modulation spaces. From this implication, we obtain the reverse square function estimate of critical order.

math.CA↗

arXiv2022

Equivalence between the energy decay of fractional damped Klein-Gordon equations and geometric conditions for damping coefficients

We consider damped $s$-fractional Klein--Gordon equations on $\mathbb{R}^d$, where $s$ denotes the order of the fractional Laplacian. In the one-dimensional case $d = 1$, Green (2020) established that the exponential decay for $s \geq 2$ and the polynomial decay of order $s/(4-2s)$ hold if and only if the damping coefficient function satisfies the so-called geometric control condition. In this note, we show that the $o(1)$ energy decay is also equivalent to these conditions in the case $d=1$. Furthermore, we extend this result to the higher-dimensional case: the logarithmic decay, the $o(1)$ decay, and the thickness of the damping coefficient are equivalent for $s \geq 2$. In addition, we also prove that the exponential decay holds for $0 < s < 2$ if and only if the damping coefficient function has a positive lower bound, so in particular, we cannot expect the exponential decay under the geometric control condition.

math.AP↗