Duality questions for operators, spectrum and measures

Thumbnail Image

Date

Authors

Journal Title

Journal ISSN

Volume Title

Publisher

Abstract

Description

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 $L^2(Ω)$ 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 $\br^n$, formulated first by Jorgensen and Pedersen.

Keywords

Functional Analysis, Classical Analysis and ODEs, 28A80, 37B50, 47A75, 46G12, 42C10.

Citation

URI

http://salesiana.dossiersoluciones.com/handle/123456789/169491

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/0809.3274
 http://arxiv.org/abs/0809.3274

Collections

arXiv