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arXiv · 0707.1766

Harmonic analysis on local fields and adelic spaces I

D. V. Osipov·A. N. Parshin
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Abstract

We develop a harmonic analysis on objects of some category $C_2$ of infinite-dimensional filtered vector spaces over a finite field. It includes two-dimensional local fields and adelic spaces of algebraic surfaces defined over a finite field. The main result is the theory of the Fourier transform on these objects and two-dimensional Poisson formulas.

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D. V. Osipov, A. N. Parshin. 2008-11-17. Harmonic analysis on local fields and adelic spaces I. https://doi.org/10.1070/im2008v072n05abeh002424

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