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Existence of fundamental solutions for Hormander operators

Published on:

28 March 2024

Primary Category:

Analysis of PDEs

Paper Authors:

Mattia Galeotti

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Key Details

Represents group G as product M x G^z, with G^z a group fiber

Defines lifted operator on G that projects to original operator on M

Shows fundamental solution for lifted operator can be saturated to obtain solution for original operator

Works for some non-simply connected manifolds

Broadens applicability of lifting techniques without nilpotency conditions

AI generated summary

Existence of fundamental solutions for Hormander operators

This paper proves that the existence of a fundamental solution for certain differential operators on a manifold follows from the existence of a fundamental solution for an associated 'lifted' operator on a Lie group. This allows techniques like 'lifting and approximation' to be applied more broadly without requiring nilpotency conditions.

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