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01 February 2006 Generic sets in spaces of measures and generic singular continuous spectrum for Delone Hamiltonians
Daniel Lenz, Peter Stollmann
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Duke Math. J. 131(2): 203-217 (01 February 2006). DOI: 10.1215/S0012-7094-06-13121-6

Abstract

We show that geometric disorder leads to some purely singular continuous spectrum generically. The main input is a result of Simon known as the Wonderland theorem in [17, Section 2]. Here we provide an alternative approach and actually a slight strengthening by showing that various sets of measures defined by regularity properties are generic in the set of all measures on a locally compact metric space. As a byproduct, we obtain the fact that a generic measure on euclidean space is singular continuous

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Daniel Lenz. Peter Stollmann. "Generic sets in spaces of measures and generic singular continuous spectrum for Delone Hamiltonians." Duke Math. J. 131 (2) 203 - 217, 01 February 2006. https://doi.org/10.1215/S0012-7094-06-13121-6

Information

Published: 01 February 2006
First available in Project Euclid: 12 January 2006

zbMATH: 1103.81017
MathSciNet: MR2219240
Digital Object Identifier: 10.1215/S0012-7094-06-13121-6

Subjects:
Primary: 81Q10 , 82B44
Secondary: 28A33 , 28C15 , 35J10

Rights: Copyright © 2006 Duke University Press

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Vol.131 • No. 2 • 01 February 2006
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