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Nonspectrality of Certain Self‐Affine Measures on ℝ3

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  • Gui-Bao Gao

Abstract

We will determine the nonspectrality of self‐affine measure μB,D corresponding to B = diag[p1, p2, p3] (p1 ∈ (2ℤ + 1)∖{±1}, p2 ∈ 2ℤ∖{0}), and D = {0, e1, e2, e3} in the space ℝ3 is supported on T(B, D), where e1, e2, and e3 are the standard basis of unit column vectors in ℝ3, and there exist at most 4 mutually orthogonal exponential functions in L2(μB,D), where the number 4 is the best. This generalizes the known results on the spectrality of self‐affine measures.

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Handle: RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:294182
DOI: 10.1155/2014/294182
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