On partially hypoelliptic operators. Part I: Differential operators

Tove Dahn

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arXiv · 1508.00530

On partially hypoelliptic operators. Part I: Differential operators

Tove Dahn

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Abstract

This article gives a fundamental discussion on variable coefficients, self-adjoint, formally partially hypoelliptic differential operators. A generalization of the results to pseudo differential operators, is given in a following article in ArXiv. Close to N. Nilsson "Some estimates for spectral functions connected with formally hypoelliptic differential operators" in Arkiv f\"or matematik ,10, 1972, we give a construction and estimates for a fundamental solution to the operator in a suitable topology. We further give estimates of the corresponding spectral kernel.

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Tove Dahn. 2015-08-03. On partially hypoelliptic operators. Part I: Differential operators. https://arxiv.org/abs/1508.00530

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