On twisted Fourier analysis and convergence of Fourier series on discrete groups

We study norm convergence and summability of Fourier series in the setting of reduced twisted group $C^*$-algebras of discrete groups. For amenable groups, F{\o}lner nets give the key to Fej\'er summation. We show that Abel-Poisson summation holds for a large class of groups, including e.g. all Coxeter groups and all Gromov hyperbolic groups. As a tool in our presentation, we introduce notions of polynomial and subexponential H-growth for countable groups w.r.t. proper scale functions, usually chosen as length functions. These coincide with the classical notions of growth in the case of amenable groups.Comment: 35 pages; abridged, revised and update

V2X Communications Applied to Safety at Level Crossings

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First application of the Laser Ion Source and Trap (LIST) for on-line experiments at ISOLDE

International audienceThe Laser Ion Source and Trap (LIST) provides a new mode of operation for the resonance ionization laser ion source (RILIS) at ISOLDE/CERN, reducing the amount of surface-ionized isobaric contaminants by up to four orders of magnitude. After the first successful on-line test at ISOLDE in 2011 the LIST was further improved in terms of efficiency, selectivity, and reliability through several off-line tests at Mainz University and at ISOLDE. In September 2012, the first on-line physics experiments to use the LIST took place at ISOLDE. The measurements of the improved LIST indicate more than a twofold increase in efficiency compared to the LIST of the 2011 run. The suppression of surface-ionized francium contaminants has enabled the first in-source laser spectroscopy of 217Po and 219Po

Charge radii and electromagnetic moments of at ^195-211At

Hyperfine-structure parameters and isotope shifts of 195–211 At have been measured for the first time at CERN-ISOLDE, using the in-source resonance-ionization spectroscopy method. The hyperfine structures of isotopes were recorded using a triad of experimental techniques for monitoring the photo-ion current. The Multi-Reflection Time-of-Flight Mass Spectrometer, in connection with a high-resolution electron multiplier, was used as an ion-counting setup for isotopes that either were affected by strong isobaric contamination or possessed a long half-life; the ISOLDE Faraday cups were used for cases with high-intensity beams; and the Windmill decay station was used for short-lived, predominantly -decaying nuclei. The electromagnetic moments and changes in the mean-square charge radii of the astatine nuclei have been extracted from the measured hyperfine-structure constants and isotope shifts. This was only made possible by dedicated state-of-the-art large-scale atomic computations of the electronic factors and the specific mass shift of atomic transitions in astatine that are needed for these extractions. By comparison with systematics, it was possible to assess the reliability of the results of these calculations and their ascribed uncertainties. A strong deviation in the ground-state mean-square charge radii of the lightest astatine isotopes, from the trend of the (spherical) lead isotopes, is interpreted as the result of an onset of deformation. This behavior bears a resemblance to the deviation observed in the isotonic polonium isotopes. Cases for shape coexistence have been identified in 197,199 At , for which a significant difference in the charge radii for ground (9/2−) and isomeric (1/2+) states has been observed