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.
