Non-spectral problem for a class of planar self-affine measures |
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Authors: | Jian-Lin Li |
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Affiliation: | College of Mathematics and Information Science, Shaanxi Normal University, Xi'an 710062, PR China |
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Abstract: | The self-affine measure μM,D corresponding to an expanding matrix M∈Mn(R) and a finite subset D⊂Rn is supported on the attractor (or invariant set) of the iterated function system {?d(x)=M−1(x+d)}d∈D. The spectral and non-spectral problems on μM,D, including the spectrum-tiling problem implied in them, have received much attention in recent years. One of the non-spectral problem on μM,D is to estimate the number of orthogonal exponentials in L2(μM,D) and to find them. In the present paper we show that if a,b,c∈Z, |a|>1, |c|>1 and ac∈Z?(3Z), |
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Keywords: | Iterated function system Self-affine measure Orthogonal exponentials Spectral measure |
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