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arXiv · 0903.1097

Fourier transform of the additive group in algebraically closed valued fields

Yimu Yin
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Abstract

We continue the study of the Hrushovski-Kazhdan integration theory and consider exponential integrals. The Grothendieck ring is enlarged via a tautological additive character and hence can receive such integrals. We then define the Fourier transform in our integration theory and establish some fundamental properties of it. Thereafter a basic theory of distributions is also developed. We construct the Weil representations in the end as an application. The results are completely parallel to the classical ones.

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Yimu Yin. 2009-03-06. Fourier transform of the additive group in algebraically closed valued fields. https://arxiv.org/abs/0903.1097

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