Spectrality of certain self‐affine measures on the generalized spatial Sierpinski gasket |
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Authors: | Qi Wang Jian‐Lin Li |
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Affiliation: | 1. +86 2. 029 3. 8531 4. 0232+86 5. 0277;6. College of Mathematics and Information Science, Shaanxi Normal University, Xi'an, P.R. China |
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Abstract: | The self‐affine measure corresponding to a upper or lower triangle expanding matrix M and the digit set in the space is supported on the generalized spatial Sierpinski gasket, where are the standard basis of unit column vectors in . We consider in this paper the existence of orthogonal exponentials on the Hilbert space , i.e., the spectrality of . Such a property is directly connected with the entries of M and is not completely determined. For this generalized spatial Sierpinski gasket, we present a method to deal with the spectrality or non‐spectrality of . As an application, the spectral property of a class of such self‐affine measures are clarified. The results here generalize the corresponding results in a simple manner. |
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Keywords: | Iterated function system (IFS) self‐affine measure orthogonal exponentials spectrality 28A80 42C05 46C05 |
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