%0 Journal Article %T Harmonic analysis on local fields and adelic spaces I %A D. V. Osipov %A A. N. Parshin %J Mathematics %D 2007 %I arXiv %R 10.1070/IM2008v072n05ABEH002424 %X 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. %U http://arxiv.org/abs/0707.1766v3