Non-spectrality of planar self-affine measures with three-elements digit set |
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Authors: | Jian-Lin Li |
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Institution: | 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 associated with an affine iterated function system {?d(x)=M−1(x+d)}d∈D is uniquely determined. The problems of determining the spectrality or non-spectrality of a measure μM,D have been 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 for an expanding integer matrix M∈M2(Z) and the three-elements digit set D given by |
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Keywords: | Iterated function system Self-affine measure Orthogonal exponentials Spectral measure |
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