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- Title
Duality Questions for Operators, Spectrum and Measures.
- Authors
Dutkay, Dorin Ervin; Jorgensen, Palle E. T.
- Abstract
We explore spectral duality in the context of measures in ℝ n, starting with partial differential operators and Fuglede’s question (1974) about the relationship between orthogonal bases of complex exponentials in L2(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 ℝ n, formulated first by Jorgensen and Pedersen.
- Subjects
DUALITY theory (Mathematics); HILBERT space; FRACTALS; TILING (Mathematics); PARTIAL differential operators; BOREL sets; FUNCTIONAL analysis; SPECTRAL theory
- Publication
Acta Applicandae Mathematicae, 2009, Vol 108, Issue 3, p515
- ISSN
0167-8019
- Publication type
Article
- DOI
10.1007/s10440-008-9427-8