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We define spherical diffraction measures for a wide class of weighted point sets in commutative spaces, i.e. proper homogeneous spaces associated with Gelfand pairs. In the case of the hyperbolic plane we can interpret the spherical diffraction measure as the Mellin transform of the auto-correlation distribution. We show that uniform regular model sets in commutative spaces have a pure point spherical diffraction measure. The atoms of this measure are located at the spherical automorphic spectrum of the underlying lattice, and the diffraction coefficients can be characterized abstractly in terms of the so-called shadow transform of the characteristic functions of the window. In the case of the Heisenberg group we can give explicit formulas for these diffraction coefficients in terms of Bessel and Laguerre functions.
We study uniform and non-uniform model sets in arbitrary locally compact second countable (lcsc) groups, which provide a natural generalization of uniform model sets in locally compact abelian groups as defined by Meyer and used as mathematical model
We study the auto-correlation measures of invariant random point processes in the hyperbolic plane which arise from various classes of aperiodic Delone sets. More generally, we study auto-correlation measures for large classes of Delone sets in (and
The Gutzwiller trace formula is extended to include diffraction effects. The new trace formula involves periodic rays which have non-geometrical segments as a result of diffraction on the surfaces and edges of the scatter.
Surface electromagnetic modes supported by metal surfaces have a great potential for uses in miniaturised detectors and optical circuits. For many applications these modes are excited locally. In the optical regime, Surface Plasmon Polaritons (SPPs)
In these lectures, we present and discuss the most recent results on inclusive diffraction at the Tevatron collider and give the prospects at the LHC. We also describe the search for exclusive events at the Tevatron. Of special interest is the exclus