On a Ring of Formal Pseudo-differential Operators

We study the notion of non-commumative higher dimensional local fields. A simplest example is the ring P of formal pseudo- differential operators. As an application we extend the KP hierarchy to the space $P^n$.Comment: LaTe

Harmonic analysis on local fields and adelic spaces I

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.Comment: 69 pages; corrected typos and inserted some changes into the last sectio