Harmonic analysis on local fields and adelic spaces.~I

D. V. Osipov ; A. N. Parshin

Izvestiya. Mathematics , Tome 72 (2008) no. 5, pp. 915-976.

Résumé

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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