Difference Sturm--Liouville problems in the imaginary direction

Yury Neretin

We consider difference operators in $L^2$ on $\mathbb{R}$ of the form $$Lf(s)=p(s)f(s+i)+q(s)f(s)+r(s)f(s-i),$$ where $i$ is the imaginary unit. The domain of definiteness are functio…