K. C. Shin
The potential $(iz)^m$ generates real eigenvalues only, under symmetric rapid decay conditions
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ABSTRACT.  We consider the eigenvalue problems 
$-u"(z)\pm (iz)^m u(z)=\lambda u(z)$, $m\geq 3$, 
under every rapid decay boundary condition that is symmetric 
with respect to the imaginary axis in the complex $z$-plane. 
We prove that the eigenvalues $\lambda$ are all positive real.