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- W2954619996 abstract "For point sets and tilings that can be constructed with the projection method, one has a good understanding of the correlation structure, and also of the corresponding spectra, both in the dynamical and in the diffraction sense. For systems defined by substitution or inflation rules, the situation is less favourable, in particular beyond the much-studied class of Pisot substitutions. In this contribution, the geometric inflation rule is employed to access the pair correlation measures of self-similar and self-affine inflation tilings and their Fourier transforms by means of exact renormalisation relations. In particular, we look into sufficient criteria for the absence of absolutely continuous spectral contributions, and illustrate this with examples from the class of block substitutions. We also discuss the Frank-Robinson tiling, as a planar example with infinite local complexity and singular continuous spectrum." @default.
- W2954619996 created "2019-07-12" @default.
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- W2954619996 date "2020-01-01" @default.
- W2954619996 modified "2023-10-16" @default.
- W2954619996 title "Renormalisation of Pair Correlations and Their Fourier Transforms for Primitive Block Substitutions" @default.
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- W2954619996 doi "https://doi.org/10.1007/978-3-030-57666-0_7" @default.
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