Laplacians on generalized smooth distributions as \(C^*\) algebra multipliers. (English) Zbl 1504.58020
Manuilov, Vladimir M. (ed.) et al., Differential equations on manifolds and mathematical physics. Dedicated to the memory of Boris Sternin. Selected papers based on the presentations of the conference on partial differential equations and applications, Moscow, Russia, November 6–9, 2018. Cham: Birkhäuser. Trends Math., 11-30 (2021).
The authors furnish a survey of results on generalized smooth distributions on manifolds, Riemannian structures, and discuss spectral properties of Laplacians associated with an arbitrary smooth distribution on a compact manifold. Next, under suitable assumptions, they prove that the Laplacian associated with the distribution defines an unbounded multiplier on the foliation \(C^\ast\)-algebra.
For the entire collection see [Zbl 1478.35002].
For the entire collection see [Zbl 1478.35002].
Reviewer: Mohammed El Aïdi (Bogotá)
MSC:
| 58J60 | Relations of PDEs with special manifold structures (Riemannian, Finsler, etc.) |
| 53C17 | Sub-Riemannian geometry |
| 46L08 | \(C^*\)-modules |
| 58B34 | Noncommutative geometry (à la Connes) |
Keywords:
foliation; Hilbert module; Laplacian; hypoelliptic operator; smooth distribution; multiplierReferences:
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