Fourier transform of the additive group in algebraically closed valued fields

• Yimu Yin ^[1]
  1. [1] Pierre and Marie Curie University

     Pierre and Marie Curie University

     París, Francia

     
• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 20, Nº. 4, 2014, págs. 1111-1157
• Idioma: inglés
• Enlaces
  • Texto completo
• Resumen

  • 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.