A nodal inverse problem for measure geometric Laplacians

Abstract

In this work we start the study of the nodal inverse problem for measure geometric Laplacians in the real line. We analyze the information contained in the set of zeros of eigenfunctions of −Δμ, and we show that it is enough to recover the support of μ. Also, we prove an uniqueness result, and we introduce a method to recover a measure ν absolutely continuous with respect to some measure μ with a continuous Radon-Nikodym derivative given the nodal points of the eigenfunctions.