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- W2344920512 abstract "Abstract For an expanding integer matrix M ∈ M n ( Z ) and two finite subsets D , S ⊂ R n of the same cardinality, the concept of compatible pair ( M − 1 D , S ) (or Hadamard triple ( M , D , S ) ) plays an important role in the spectrality of self-affine measure μ M , D . It is known that ( M − 1 D , S ) is a compatible pair if and only if ( M ⁎ − 1 S , D ) is a compatible pair. An old duality conjecture of Dutkay and Jorgensen states that under the condition of compatible pair ( M − 1 D , S ) , μ M , D is a spectral measure if and only if μ M ⁎ , S is. In this paper, we construct an example of compatible pair ( M − 1 D , S ) to illustrate that the self-affine measure μ M , D is a spectral measure but the self-affine measure μ M ⁎ , S is not. This disproves the above-mentioned conjecture of Dutkay and Jorgensen, and clarifies certain dual relation on the spectrality of self-affine measures." @default.
- W2344920512 created "2016-06-24" @default.
- W2344920512 creator A5011631250 @default.
- W2344920512 date "2016-10-01" @default.
- W2344920512 modified "2023-10-03" @default.
- W2344920512 title "A counterexample to Dutkay–Jorgensen conjecture" @default.
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- W2344920512 doi "https://doi.org/10.1016/j.jmaa.2016.04.065" @default.
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