2019/10/07 by Iakovos Androulidakis, Androulidakis, Iakovos, Omar Mohsen +3
Mathematics · #Advanced Banach Space Theory #Advanced Operator Algebra Research #Advanced Topics in Algebra #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #Dynamical Systems (math.DS) #FOS: Mathematics
paper · pdf · doi:10.48550/arxiv.1910.02623
openalex publication_date 2019/10/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Motivated by the study of Hörmander's sums-of-squares operators and their generalizations, we define the convolution algebra of transverse distributions associated to a singular foliation. We prove that this algebra is represented as continuous linear operators on the spaces of smooth functions and generalized functions on the underlying manifold, and on the leaves and their holonomy covers. This generalizes Schwartz kernel operators to singular foliations. We also define the algebra of smoothing operators in this context and prove that it is a two-sided ideal.