The convolution algebra of Schwarz kernels on a singular foliation
Citation:
Androulidakis I, Mohsen O, Yuncken R. The convolution algebra of Schwarz kernels on a singular foliation. J. OPERATOR THEORY [Internet]. 2021;85(2):475-503.
Motivated by the study of Hörmander's sums-of-squares operators and their generalizations, we define the convolution algebra of proper 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. 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.
National and Kapodistrian University of Athens, Department of Mathematics (+30) 210-7276423 Panepistimiopolis Zografou Athens, ZipCode 157-84 iandroul@math.uoa.gr
