On the heat kernel of the Rumin complex and Calderón reproducing formula

Abstract

We derive several properties of the heat equation with the Hodge operator associated with the Rumin’s complex on Heisenberg groups and prove several properties of the fundamental solution. As an application, we use the heat kernel for Rumin’s differential forms to construct a Calderón reproducing formula on Rumin’s forms.

Keywords

• heisenberg groups
• differential forms
• currents
• laplace operators
• heat kernel
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