4 papers
Extremality and designs in spaces of quadratic forms
Claude Pache
A well known theorem of Voronoi caracterizes extreme quadratic forms and Euclidean lattices, that is those which are local maxima for the Hermite function, as perfect and eutactic.…
Construction of spherical cubature formulas using lattices
Pierre De La Harpe, Claude Pache, Boris B. Venkov
We construct cubature formulas on spheres supported by homothetic images of shells in some Euclidian lattices. Our analysis of these cubature formulas uses results from the theory…
Shells of selfdual lattices viewed as spherical designs
Claude Pache
We find out for which shells of selfdual lattices and of theirs shadows are spherical -designs. The method uses theta series of lattices, which are modular forms. We analyse…
Cubature formulas, geometrical designs, reproducing kernels, and Markov operators
Pierre De La Harpe, Claude Pache
Cubature formulas and geometrical designs are described in terms of reproducing kernels for Hilbert spaces of functions on the one hand, and Markov operators associated to orthogon…