P. Stinga

The equivalence of solutions to fractional and logarithmic Helmholtz equations

We show the following equivalence of solutions to general fractional Helmholtz equations: $u$ is a solution to $$A^su=\lambda^su$$ for \textit{some} fixed $00$ if and only if $u$ is a solution to the same equation for \textit{all} $s\neq0$. Furthermore, we show as well that $u$ equivalently solves the logarithmic Helmh...