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Learning is but an adjunct to ourself And where we are our learning likewise is. Abstract The paper studies ways in which the sets of a partition of a lattice in R n become regular model sets. The main theorem gives equivalent conditions which assure that a matrix substitution system on a lattice in R n gives rise to regular model sets (based on p-adic-like… (More)

We prove that the set of visible points of any lattice of dimension n ≥ 2 has pure point diffraction spectrum, and we determine the diffraction spectrum explicitly. This settles previous speculation on the exact nature of the diffrac-tion in this situation. Using similar methods we show the same result for the 1-dimensional set of kth-power-free integers… (More)

- Yuly Billig, S Eswara Rao, R V Moody
- 2008

Vertex operators discovered by physicists in string theory have turned out to be important objects in mathematics. One can use vertex operators to construct various realizations of the irreducible highest weight representations for affine Kac-Moody algebras. Two of these, the principal and homogeneous realizations, are of particular interest. The principal… (More)

This paper develops a method for discrete computational Fourier analysis of functions defined on quasicrystals and other almost periodic sets. A key point is to build the analysis around the emerging theory of quasicrystals and diffraction in the setting on local hulls and dynamical systems. Numerically computed approximations arising in this way are built… (More)

A linear deformation of a Meyer set M in R d is the image of M under a group homomorphism of the group [M ] generated by M into R d. We provide a necessary and sufficient condition for such a deformation to be a Meyer set. In the case that the deformation is a Meyer set and the deformation is injective, the deformation is pure point diffractive if the… (More)

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