Duality Questions for Operators, Spectrum and Measures

• Dorin Ervin Dutkay ^[1] ; Palle E. T. Jorgensen ^[2]
  1. [1] University of Central Florida

     University of Central Florida

     Estados Unidos

     
  2. [2] University of Iowa

     University of Iowa

     City of Iowa City, Estados Unidos

     
• Localización: Acta applicandae mathematicae, ISSN 0167-8019, Vol. 108, Nº. 3, 2009 (Ejemplar dedicado a: Analysis on Fractals, Wavelets, Dynamical Systems, and Quantum Information), págs. 515-528
• Idioma: inglés
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• Resumen

  • We explore spectral duality in the context of measures in ℝn, 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 ℝn, formulated first by Jorgensen and Pedersen.