Spectra of Sub-Dirac Operators on Certain Nilmanifolds

• Autores: Ines Kath, Oliver Ungermann
• Localización: Mathematica scandinavica, ISSN 0025-5521, Vol. 117, Nº 1, 2015, págs. 64-104
• Idioma: inglés
• DOI: 10.7146/math.scand.a-22237
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• Resumen

  • 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.