Hadamard三元组生成自仿射谱测度
Hadamard triples generate self-affine spectral measures
摘要：
设$R$是一个整数扩张矩阵，$B,L$是一个有限整数数集，使得$(R,B,L)$在${\br}^d$上形成一个Hadamard三元组.证明了伴随的自仿射测度$μ= μ(R,B)$是谱测度，这意味着它在$L^2(μ)$中存在指数函数的规范正交基.这解决了一个长期存在的猜想提出的约根森和彼得森和研究的许多其他作者。
英文摘要：
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 $L^2(μ)$. This settles a long-standing conjecture proposed by Jorgensen and Pedersen and studied by many other authors.
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