Geodesic
Harmonic analysis on local fields and adelic spaces. II
Izvestiya. Mathematics , Tome 75 (2011) no. 4, pp. 749-814.

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We develop harmonic analysis in certain categories of filtered Abelian groups and vector spaces. The objects of these categories include local fields and adelic spaces arising from arithmetic surfaces. We prove some structure theorems for quotients of the adèle groups of algebraic and arithmetic surfaces.
Keywords: arithmetic surfaces, higher adèles, harmonic analysis
Mots-clés : Fourier transform, Poisson summation formulae. 
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D. V. Osipov; A. N. Parshin. Harmonic analysis on local fields and adelic spaces. II. Izvestiya. Mathematics , Tome 75 (2011) no. 4, pp. 749-814. http://geodesic.mathdoc.fr/item/IM2_2011_75_4_a4/

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