Fourier transform of the additive group in algebraically closed valued fields

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.

References in corpus (6)

• Iwahori-Hecke Algebras
• Transfer Principle for the Fundamental Lemma
• Quantifier elimination and minimality conditions in algebraically closed valued fields
• Motivic Poisson summation
• Integration in algebraically closed valued fields
• Special transformations in algebraically closed valued fields

Cited by in corpus (5)

• Quantifier elimination and minimality conditions in algebraically closed valued fields
• Additive invariants in o-minimal valued fields
• Motivic wave front sets
• Integration in power-bounded $T$-convex valued fields
• $T$-convex valued fields with tempered exponentiation