Geodesic
Harmonic analysis on local fields and adelic spaces.~I
Izvestiya. Mathematics , Tome 72 (2008) no. 5, pp. 915-976

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We develop harmonic analysis on the objects of a category $C_2$ of infinite-dimensional filtered vector spaces over a finite field. This category includes two-dimensional local fields and adelic spaces of algebraic surfaces defined over a finite field. As the main result, we construct the theory of the Fourier transform on these objects and obtain two-dimensional Poisson formulae. 
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     author = {D. V. Osipov and A. N. Parshin},
     title = {Harmonic analysis on local fields and adelic {spaces.~I}},
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     url = {http://geodesic.mathdoc.fr/item/IM2_2008_72_5_a2/}
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D. V. Osipov; A. N. Parshin. Harmonic analysis on local fields and adelic spaces.~I. Izvestiya. Mathematics , Tome 72 (2008) no. 5, pp. 915-976. http://geodesic.mathdoc.fr/item/IM2_2008_72_5_a2/