Duality Questions for Operators, Spectrum and Measures
Abbreviated Journal Title
Acta Appl. Math.
Spectrum; Hilbert space; Orthogonal basis; Fractal; Tiling; SELF-AFFINE TILES; PARTIAL-DIFFERENTIAL OPERATORS; ITERATED FUNCTION; SYSTEMS; DENSE ANALYTIC SUBSPACES; WEYL-BERRY CONJECTURE; MOCK; FOURIER-SERIES; FUGLEDES CONJECTURE; SET CONJECTURE; FRACTAL DRUMS; UNIVERSAL SPECTRA; Mathematics, Applied
We explore spectral duality in the context of measures in a"e (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 a"e (n) , formulated first by Jorgensen and Pedersen.
Acta Applicandae Mathematicae
"Duality Questions for Operators, Spectrum and Measures" (2009). Faculty Bibliography 2000s. 1502.