Spectra of sub-Dirac operators on certain nilmanifolds

Ines Kath; Oliver Ungermann

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arXiv · 1311.2418

Spectra of sub-Dirac operators on certain nilmanifolds

Ines Kath·Oliver Ungermann

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Abstract

We study sub-Dirac operators that are associated with left-invariant bracket-generating sub-Riemannian structures on compact quotients of nilpotent semi-direct products $G=\mathbb{R}^n\rtimes_A\mathbb{R}$. We will prove that these operators admit an $L^2$-basis of eigenfunctions. Explicit examples show that the spectrum of these operators can be non-discrete and that eigenvalues may have infinite multiplicity.

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Ines Kath, Oliver Ungermann. 2013-11-11. Spectra of sub-Dirac operators on certain nilmanifolds. https://arxiv.org/abs/1311.2418

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