English

Duality questions for operators, spectrum and measures

Functional Analysis 2008-09-22 v1 Classical Analysis and ODEs

Abstract

We explore spectral duality in the context of measures in \brn\br^n, starting with partial differential operators and Fuglede's question (1974) about the relationship between orthogonal bases of complex exponentials in L2(Ω)L^2(\Omega) and tiling properties of Ω\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 \brn\br^n, formulated first by Jorgensen and Pedersen.

Keywords

Cite

@article{arxiv.0809.3274,
  title  = {Duality questions for operators, spectrum and measures},
  author = {Dorim Ervin Dutkay and Palle E. T. Jorgensen},
  journal= {arXiv preprint arXiv:0809.3274},
  year   = {2008}
}
R2 v1 2026-06-21T11:21:52.085Z