Geodesic
Unboundedness of a $p$-adic Gaussian distribution
Izvestiya. Mathematics , Tome 41 (1993) no. 2, pp. 367-375.

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The intensive development of mathematical physics over non-Archimedean number fields has led to the emergence of many new mathematical constructions. In particular, a $p$-adic Gaussian distribution was introduced that lies at the basis of $p$-adic quantum mechanics with $p$-adic-valued functions. In this paper it is proved that, in contrast to the real theory, a Gaussian distribution in the $p$-adic case is not a measure, and the corresponding linear functional is unbounded on the space of continuous functions. 
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A. Yu. Khrennikov; M. Endo. Unboundedness of a $p$-adic Gaussian distribution. Izvestiya. Mathematics , Tome 41 (1993) no. 2, pp. 367-375. http://geodesic.mathdoc.fr/item/IM2_1993_41_2_a9/

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