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 , starting with partial differential operators and Fuglede's question (1974) about the relationship between orthogonal bases of complex exponentials in and tiling properties of , 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 , 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}
}