Helmholtz Solutions for the Fractional Laplacian and Other Related Operators

Vincent Guan, Mathav Murugan, Juncheng Wei

We show that the bounded solutions to the fractional Helmholtz equation, $(-\Delta {)}^{s}u=u$ for $0<s<1$ in ${\mathbb{R}}^n$, are given by the bounded solutions to the classical Helmholtz…