Kochubei A.N.
p-ADIC COMMUTATION RELATIONS
(12K, AMS-TeX)
ABSTRACT. Representations of the canonical and deformed commutation relations
by bounded operators on $p$-adic Banach spaces are constructed.
Functions from the Mahler basis of the space of $p$-adic continuous
functions and their multiplicative analogues are shown to be the
$p$-adic counterparts of the Hermite and $q$-Hermite functions.
The analogue of the Stone-von Neumann uniqueness theorem fails
in the $p$-adic case.