Completeness of generalized transmission eigenstates
Eemeli Bl{\aa}sten, Lassi P\"aiv\"arinta
TL;DR
This paper proves that generalized transmission eigenstates form a complete set for acoustic and Schrödinger equations, using advanced ellipticity theory, which enhances understanding of spectral properties in inverse problems.
Contribution
It establishes the completeness of generalized transmission eigenstates for specific PDEs using ellipticity theory, a novel approach in this context.
Findings
Proves completeness of eigenstates for acoustic equations
Proves completeness of eigenstates for Schrödinger equations
Uses ellipticity theory of Agranovich and Vishik
Abstract
We prove the completeness of the generalized (interior) transmission eigenstates for the acoustic and Schr\"odinger equations. The method uses the ellipticity theory of Agranovich and Vishik.
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