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Laplacians for generalised smooth distributions as C*-algebra multipliers

Citation:

Androulidakis I, Kordyukov Y. Laplacians for generalised smooth distributions as C*-algebra multipliers. In: Manuilov, V.M., Mishchenko, A.S., Nazaikinskii, V.E., Schulze, BW., Zhang, W. (eds) Differential Equations on Manifolds and Mathematical Physics. . Trends in Mathematics. Birkhäuser, Cham.; 2021. pp. 11-30.
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Abstract:

In this paper, we discuss spectral properties of Laplacians associated with an arbitrary smooth distribution on a compact manifold. First, we give a survey of results on generalized smooth distributions on manifolds, Riemannian structures and associated Laplacians. Then, under the assumption that the singular foliation generated by the distribution is regular, we prove that the Laplacian associated with the distribution defines an unbounded multiplier on the foliation C*-algebra. To this end, we give the construction of a parametrix.

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