On the transfer of information in multiplier equations

arXiv1912.10760MaRDI QIDQ6331668

David Scott Winterrose, Mirza Karamehmedović

Publication date: 23 December 2019

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.

Mathematics Subject Classification ID

Boundary value problems for higher-order elliptic equations (35J40) Boundary value problems for PDEs with pseudodifferential operators (35S15) Green's functions for elliptic equations (35J08)

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