Delve into the future of research at MiS with our preprint repository. Our scientists are making groundbreaking discoveries and sharing their latest findings before they are published. Explore repository to stay up-to-date on the newest developments and breakthroughs.
Spectral Estimates and Non-Selfadjoint Perturbations of Spheroidal Wave Operators
Felix Finster and Harald Schmid
We derive a spectral representation for the oblate spheroidal wave operator, which is holomorphic in the aspherical parameter $\Omega$ in a neighborhood of the real line. For real $\Omega$, estimates are derived for all eigenvalue gaps uniformly in~$\Omega$.
The proof of the gap estimates is based on detailed estimates for complex solutions of the Riccati equation. The spectral representation for complex $\Omega$ is derived using the theory of slightly non-selfadjoint perturbations.