Quantization of the affine group of a local field

2017/02/06 by Victor Gayral, Gayral, Victor, David Jondreville +1
Mathematics · #Advanced Algebra and Geometry #FOS: Mathematics #FOS: Physical sciences #Functional Analysis (math.FA) #Mathematical Analysis and Transform Methods #Mathematical Physics (math-ph) #Operator Algebras (math.OA) #advanced mathematical theories

paper · doi:10.48550/arxiv.1702.01542

openalex publication_date 2017/02/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For a non Archimedean local field which is not of characteristic 2, nor an extension of \mathbb Q₂, 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 generalisation 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.

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