Institute of Mathematics of NAS of Ukraine,
3 Tereshchenkivs'ka Str.,
01601 Kyiv-4, UKRAINE

Constructions of non-Gaussian measures on the space of distributions over the field of p-adic numbers

We construct measures on the space D(Qpn), n 4, of Bruhat-Schwartz distributions over the field of p-adic numbers, corresponding to finite volume interactions in a p-adic analog of the Euclidean quantum field theory. In contrast to earlier results in this direction, our choice of the free measure is the Gaussian measure corresponding to an elliptic pseudo-differential operator over Qpn.