Harmonic analysis on local fields and adelic spaces I

Details Harmonic analysis on local fields and adelic spaces I Harmonic analysis on local fields and adelic spaces I

2007-07-12

arxiv.org/abs/0707.1766v3

Izvestiya: Mathematics, 2008, 72:5, pp. 915-976

Mathematics

Algebraic Geometry

69 pages; corrected typos and inserted some changes into the last section

Scientific paper

10.1070/IM2008v072n05ABEH002424

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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