Quantization of the affine group of a local field

  • Victor Gayral

    Université de Reims Champagne-Ardennes, Reims, France
  • David Jondreville

    Université de Reims Champagne-Ardennes, Reims, France
Quantization of the affine group of a local field cover

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Abstract

For a non-Archimedean local field which is not of characteristic 2, nor an extension of , we construct a pseudo-differential calculus covariant under a unimodular subgroup of the affine group of the field. Our phase space is a quotient group of the covariance group. Our main result is a generalization on that context of the Calderón–Vaillancourt estimate. Our construction can be thought as the non-Archimedean version of Unterberger’s Fuchs calculus and our methods are mainly based on Wigner functions and on coherent states transform.

Cite this article

Victor Gayral, David Jondreville, Quantization of the affine group of a local field. J. Fractal Geom. 6 (2019), no. 2, pp. 157–204

DOI 10.4171/JFG/74