Quantizations and symbolic calculus over the $p$-adic numbers

Haran, Shai

Annales de l'Institut Fourier, Tome 43 (1993) no. 4, pp. 997-1053.

Nous développons la théorie du calcul symbolique des opérateurs pseudo-différentiels de Weyl sur les nombres $p$-adiques. Nous appliquons cette théorie à l’étude des opérateurs globalement elliptiques sur les nombres $p$-adiques et nous déterminons de façon exacte le comportement asymptotique de leur spectre.

We develop the basic theory of the Weyl symbolic calculus of pseudodifferential operators over the $p$-adic numbers. We apply this theory to the study of elliptic operators over the $p$-adic numbers and determine their asymptotic spectral behavior.

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