Spectra of Sub-Dirac Operators on Certain Nilmanifolds - Kath, Ines; Ungermann, Oliver (MATHEMATICA SCANDINAVICA, 2015)
We study sub-Dirac operators associated to left-invariant bracket-generating sub-Riemannian structures on compact quotients of nilpotent semi-direct products G=R^n times_AR. We prove that these operators admit an L^2-basis of eigenfunctions. Explicit examples of this type show that the spectrum of these operators can be non-discrete and that eigenvalues may have infinite multiplicity. In this case the sub-Dirac operator is neither Fredholm nor hypoelliptic.