Tomoyuki Kakehi

activity

20042025

collaborators

5 papers

math.AP2025

The Snapshot Problem for the Euler-Poisson-Darboux Equation

Fulton Gonzalez, Jue Wang, Jens Christensen +1

The generalized Euler-Poisson-Darboux (EPD) equation with complex parameter $α$ is given by $$ Δ_x u=\frac{\partial^2 u}{\partial t^2}+\frac{n-1+2α}{t}\,\frac{\partial u}{\partial…

math.AP2023

The Snapshot Problem for the Wave equation

Fulton Gonzalez, Tomoyuki Kakehi, Jens Christensen +1

By definition, a wave is a $C^{\infty}$ solution $u (x, t)$ of the wave equation on $R^{n}$ , and a snapshot of the wave $u$ at time $t$ is the function $u_{t}$ on $R^{n}$ giv…

math.FA2020

Surjectivity of Convolution Operators on Noncompact Symmetric Spaces

Fulton Gonzalez, Tomoyuki Kakehi, Jue Wang

Let $μ$ be a $K$ -invariant compactly supported distribution on a noncompact Riemannian symmetric space $X = G / K$ . If the spherical Fourier transform $μ (λ)$ is slowly decrea…

math.FA2016

Surjectivity of Mean Value Operators on Noncompact Symmetric Spaces

Jens Christensen, Fulton Gonzalez, Tomoyuki Kakehi

Let $X = G / K$ be a symmetric space of the non-compact type. We prove that the mean value operator over translated $K$ -orbits of a fixed point is surjective on the space of smooth fun…

math.FA2004

Moment Conditions and Support Theorems for Radon Transforms on Affine Grassmann Manifolds

Fulton B. Gonzalez, Tomoyuki Kakehi

Let $G (p, n)$ and $G (q, n)$ be the affine Grassmann manifolds of $p$ - and $q$ - planes in $R^{n}$ , respectively, and let $R^{(p, q)}$ be the Radon transform from smoo…