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dc.contributor.advisorSolomyak, Borisen_US
dc.contributor.authorBartlett, Alanen_US
dc.date.accessioned2015-09-29T21:24:45Z
dc.date.available2015-09-29T21:24:45Z
dc.date.submitted2015en_US
dc.identifier.otherBartlett_washington_0250E_15052.pdfen_US
dc.identifier.urihttp://hdl.handle.net/1773/34019
dc.descriptionThesis (Ph.D.)--University of Washington, 2015en_US
dc.description.abstractIn this paper, we generalize and develop results of Queffelec allowing us to characterize the spectrum of an aperiodic substitution in Z^d by describing the Fourier coefficients of mutually singular measures of pure type giving rise to the maximal spectral type of the translation operator on L^2. This is done without any assumptions on primitivity or height, and provides a simple algorithm for determining singularity to Lebesgue spectrum for such substitutions, and we use this to show singularity of the spectrum for Queffelec's noncommutative bijective substitution, as well as the Table tiling, answering an open question of Solomyak. Moreover, we also prove that the spectrum of any aperiodic bijective commutative Z^d substitution on a finite alphabet is purely singular. Finally, we show that every ergodic matrix of measures on a compact metric space can be diagonalized, which we use in the proof of the main result.en_US
dc.format.mimetypeapplication/pdfen_US
dc.language.isoen_USen_US
dc.rightsCopyright is held by the individual authors.en_US
dc.subjectErgodic Theory; Spectral Theory; Substitutionsen_US
dc.subject.otherMathematicsen_US
dc.subject.othermathematicsen_US
dc.titleSpectral Theory of Z^d Substitutionsen_US
dc.typeThesisen_US
dc.embargo.termsOpen Accessen_US


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