Resumen de Duality Questions for Operators, Spectrum and Measures

Dorin Ervin Dutkay, Palle E. T. Jorgensen

• We explore spectral duality in the context of measures in ℝn, 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 ℝn, formulated first by Jorgensen and Pedersen.