Year: 2023
Type: preprint
Abstract: In this article, we classify all distributional solutions of $f(-Δ)u=f(1)u$ where $f$ is a non-constant Bernstein function. Specifically, we show that the Fourier transform of $u$ is a single-layer distribution on the unit sphere. Examples of such operators include $(-Δ)^σ$ (for $σ\in (0,1]$), $\log(1-Δ)$ and $(-Δ)^\frac{1}{2}\text{tanh}((-Δ)^\frac{1}{2})$.
Source: arXiv (Cornell University)
Authors: Hauer, Daniel, Lee, David
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4383046895