Spectra of Sub-Dirac Operators on Certain Nilmanifolds

  • Ines Kath
  • Oliver Ungermann

Abstract

We study sub-Dirac operators associated to left-invariant bracket-generating sub-Riemannian structures on compact quotients of nilpotent semi-direct products $G=\mathsf{R}^n\rtimes_A\mathsf{R}$. 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.
Published
2015-09-28
How to Cite
Kath, I., & Ungermann, O. (2015). Spectra of Sub-Dirac Operators on Certain Nilmanifolds. MATHEMATICA SCANDINAVICA, 117(1), 64-104. https://doi.org/10.7146/math.scand.a-22237
Section
Articles