Fourier transform of the additive group in algebraically closed valued fields - Mathematics > LogicReport as inadecuate




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Abstract: We continue the study of the Hrushovski-Kazhdan integration theory andconsider exponential integrals. The Grothendieck ring is enlarged via atautological additive character and hence can receive such integrals. We thendefine the Fourier transform in our integration theory and establish somefundamental properties of it. Thereafter a basic theory of distributions isalso developed. We construct the Weil representations in the end as anapplication. The results are completely parallel to the classical ones.



Author: Yimu Yin

Source: https://arxiv.org/







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