Robert V. Moody

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This article surveys the mathematics of the cut and project method as applied to point sets, called here model sets. It covers the geometric, arithmetic, and analytical sides of this theory as well as diffraction and the connection with dynamical systems. Dedicated to the memory of Richard (Dick) Slansky The spirit of the universe is subtle and informs all(More)
We consider two dynamical systems associated with a substitution of Pisot type: the usual Z-action on a sequence space, and the R-action, which can be defined as a tiling dynamical system or as a suspension flow. We describe procedures for checking when these systems have pure discrete spectrum (the “balanced pairs algorithm” and the “overlap algorithm”)(More)
Similar sublattices of the root lattice A4 are possible [9] for each index that is the square of a non-zero integer of the form m + mn − n. Here, we add a constructive approach, based on the arithmetic of the quaternion algebra H(Q( √ 5)) and the existence of a particular involution of the second kind, which also provides the actual sublattices and the(More)
The paper is about methods of discrete Fourier analysis in the context of Weyl group symmetry. Three families of class functions are defined on the maximal torus of each compact simply connected semisimple Lie group G. Such functions can always be restricted without loss of information to a fundamental region F̌ of the affine Weyl group. The members of each(More)