2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/169491We explore spectral duality in the context of measures in $\br^n$, starting with partial differential operators and Fuglede's question (1974) about the relationship between orthogonal bases of complex exponentials in $L^2(Ω)$ and tiling properties of $Ω$, then continuing with affine iterated function systems. We review results in the literature from 1974 up to the present, and we relate them to a general framework for spectral duality for pairs of Borel measures in $\br^n$, formulated first by Jorgensen and Pedersen.Functional AnalysisClassical Analysis and ODEs28A80, 37B50, 47A75, 46G12, 42C10.text