Explicit diagonalization of the linearized Calderón problem on the disk: multiplicity normalization and exponential spectral attenuation

Abstract

We study the full angular dependence of the linearized Schrödinger form of the Calderón problem on the unit disk. We obtain an explicit continuous spectral diagonalization of its normal operator and hence a generalized singular system for the linearized forward map. To our knowledge, this is the first such diagonalization for the full angularly dependent, multiplicity-normalized linearized measurement map on the disk.