Duality questions for operators, spectrum and measures

Details Duality questions for operators, spectrum and measures Duality questions for operators, spectrum and measures

2008-09-19

arxiv.org/abs/0809.3274v1

Mathematics

Functional Analysis

Scientific paper

We 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 $L^2(\Omega)$ and tiling properties of $\Omega$, 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.

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