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arXiv · 1912.10760

On the transfer of information in multiplier equations

Mirza Karamehmedović·David Winterrose
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Abstract

We derive spectral width estimates for traces of tempered solutions of a large class of multiplier equations in $\mathbf{R}^n$. The estimates are uniform for solutions up to a given order. In the process, we find a rather explicit expression for a tempered fundamental solution of a multiplier. We successfully verify our spectral width estimates against numerical results in several scenarios involving the inhomogeneous Helmholtz equation in $\mathbf{R}^n$ with $n=1,\dots,9$. Our main result is directly applicable in the stability analysis of solutions of inverse source problems.

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Mirza Karamehmedović, David Winterrose. 2019-12-23. On the transfer of information in multiplier equations. https://arxiv.org/abs/1912.10760

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