Differences between fundamental solutions of general higher order elliptic operators and of products of second order operators

@article{Grunau2019DifferencesBF,
  title={Differences between fundamental solutions of general higher order elliptic operators and of products of second order operators},
  author={Hans-Christoph Grunau and Giulio Romani and Guido Sweers},
  journal={Mathematische Annalen},
  year={2019},
  pages={1-54}
}
We study fundamental solutions of elliptic operators of order $$2m\ge 4$$ 2 m ≥ 4 with constant coefficients in large dimensions $$n\ge 2m$$ n ≥ 2 m , where their singularities become unbounded. For compositions of second order operators these can be chosen as convolution products of positive singular functions, which are positive themselves. As soon as $$n\ge 3$$ n ≥ 3 , the polyharmonic operator $$(-\Delta )^m$$ ( - Δ ) m may no longer serve as a prototype for the general elliptic operator… Expand
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