Hadamard triples generate self-affine spectral measures

2015/06/04 by Dutkay, Dorin Ervin, Lai, Chun-Kit, Haussermann, John · 4 citations
#FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.1506.01503

Abstract

Let R be an expanding matrix with integer entries and let B,L be finite integer digit sets so that (R,B,L) form a Hadamard triple on \br^d. We prove that the associated self-affine measure μ= μ(R,B) is a spectral measure, which means it admits an orthonormal bases of exponential functions in L²(μ). This settles a long-standing conjecture proposed by Jorgensen and Pedersen and studied by many other authors.

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