Gilbert Muraz

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We study lower bounds of the packing density of a system of nonoverlapping equal spheres in Rn, n ≥ 2, as a function of the maximal circumradius of its Voronoi cells. Our viewpoint is that of Delone sets which allows to investigate the gap between the upper bounds of Rogers or Kabatjanskĭi-Levens̆tein and the Minkowski-Hlawka type lower bounds for the(More)
The set UDr of point sets of R, n ≥ 1, having the property that their minimal interpoint distance is greater than a given strictly positive constant r > 0 is shown to be equippable by a metric for which it is a compact topological space and such that the Hausdorff metric on the subset UDr,f ⊂ UDr of the finite point sets is compatible with the restriction(More)
In this note, the authors illustrate how compact embeddings between function spaces can be obtained using wavelet methods. They consider weighted Hölder spaces and obtain optimal growth conditions on the wavelet coefficients for functions in these weighted spaces. These conditions lead to continuous embeddings between weighted Hölder spaces and certain(More)
We investigate, by “ à la Marcinkiewicz” techniques applied to the (asymptotic) density function, how dense systems of equal spheres of Rn, n ≥ 1, can be partitioned at infinity in order to allow the computation of their density as a true limit and not a limsup. The density of a packing of equal balls is the norm 1 of the characteristic function of the(More)
We give the construction of a metric, invariant by the group of rigid motions of R, on the set of uniformly discrete point sets of R, n > 1, of given constant, i.e. having the property that their minimal interpoint distance is greater than a given strictly positive real number. The corresponding metric space is complete and locally compact. As a(More)
Let A be a commutative algebra of operators on a Banach space. For each x ∈ X and a ∈ A, we introduce their local spectra Sp(x) and Sp(a) as subsets of the maximal ideal space M of A, and for each subset Λ ⊂ M we define the spectral subspace X(Λ) consisting of x with Sp(x) ⊂ Λ. The main result of the paper states that if A is a regular, not necessarily(More)
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