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Pré-Publication, Document De Travail Année : 2019

THE CONVOLUTION ALGEBRA OF SCHWARTZ KERNELS ON A SINGULAR FOLIATION

Résumé

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.
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Dates et versions

hal-02359878 , version 1 (12-11-2019)

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  • HAL Id : hal-02359878 , version 1

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Iakovos Androulidakis, Omar Mohsen, Robert Yuncken. THE CONVOLUTION ALGEBRA OF SCHWARTZ KERNELS ON A SINGULAR FOLIATION. 2019. ⟨hal-02359878⟩
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