Laplacians on generalized smooth distributions as C^*-algebra\n multipliers

2019/02/07 by Iakovos Androulidakis, Androulidakis, Iakovos, Yuri A. Kordyukov +1
Mathematics · #Advanced Operator Algebra Research #Advanced Topics in Algebra #Differential Geometry (math.DG) #FOS: Mathematics #Operator Algebras (math.OA) #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.1902.03139

openalex publication_date 2019/02/07 · openalex created_date 2022/10/02 · openalex updated_date 2026/07/28

Abstract

In this paper, we discuss spectral properties of Laplacians associated with\nan arbitrary smooth distribution on a compact manifold. First, we give a survey\nof results on generalized smooth distributions on manifolds, Riemannian\nstructures and associated Laplacians. Then, under the assumption that the\nsingular foliation generated by the distribution is regular, we prove that the\nLaplacian associated with the distribution defines an unbounded multiplier on\nthe foliation C^*-algebra. To this end, we give the construction of a\nparametrix.\n

Related

• Riemannian metrics and Laplacians for generalised smooth distributions
• Geometrical embeddings for distributions into algebras of generalized functions
• Energy of generalized distributions
• Foliation C*-algebras on multiply fibred manifolds
• The convolution algebra of Schwarz kernels on a singular foliation