Decay of eigenfunctions of elliptic PDE's

By I. Herbst and E. Skibsted
No. 03, August 2013

We study exponential decay of eigenfunctions of self-adjoint higher order elliptic operators on $\mathbb{R}^d$. We show that the possible critical decay rates are determined algebraically. In addition we show absence of super-exponentially decaying eigenfunctions and a refined exponential upper bound.

Keywords: eigenfunctions, exponential decay, microlocal analysis, combinatorics.

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