Harmonic analysis over adelic spaces
نویسنده
چکیده
In [4], D. Osipov and A. Parshin developed an approach to harmonic analysis on higher dimensional local fields through categories of filtered vector spaces as in [3]. In the present paper we give a variant of this approach that behaves nicely for inductive arguments. We establish Pontryagin duality, the Fourier inversion formula, and a Plancherel formula for all dimensions. ∗This paper was written during a stay of the author at the Hausdorff Research Institute for Mathematics, Bonn. The author expresses his gratitude for the warm hospitality and the possibility to enjoy the inspiring atmosphere of this place.
منابع مشابه
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.
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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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