Scaling of the Thue–Morse diffraction measure
نویسندگان
چکیده
The Thue–Morse (TM) sequence is defined via the binary substitution 1 7→ 11̄, 1̄ 7→ 1̄1; see [1, 4] and references therein for general background. The corresponding dynamical system is known to have mixed (pure point and singular continuous) spectrum [12, 15, 17], with a pure point part on the dyadic points and a singular continuous spectral measure in the form of a Riesz product. The latter coincides with the diffraction measure γ̂ of the TM Dirac comb with weights ±1; compare [2] for details. The Riesz product representation of the TM diffraction measure reads
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