Geodesic
Construction of Interaction Measures on the Space of Distributions over the Field of $p$-Adic Numbers
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Selected topics of $p$-adic mathematical physics and analysis, Tome 245 (2004), pp. 146-153

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We overview the construction of non-Gaussian measures on the space $\mathcal D'(\mathbb Q_p^n)$, $n\le 4$, of Bruhat–Schwartz distributions over the field of $p$-adic numbers, corresponding to finite volume polynomial interactions in a $p$-adic analogue of the Euclidean quantum field theory. Our choice of the free measure is the Gaussian measure corresponding to an elliptic pseudodifferential operator over $\mathbb Q_p^n$. Analogues of the Euclidean $P(\varphi)$-theories with free and half-Dirichlet boundary conditions are considered. 
@article{TM_2004_245_a14,
     author = {A. N. Kochubei and M. R. Sait-Ametov},
     title = {Construction of {Interaction} {Measures} on the {Space} of {Distributions} over the {Field} of $p${-Adic} {Numbers}},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {146--153},
     publisher = {mathdoc},
     volume = {245},
     year = {2004},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TM_2004_245_a14/}
}
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A. N. Kochubei; M. R. Sait-Ametov. Construction of Interaction Measures on the Space of Distributions over the Field of $p$-Adic Numbers. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Selected topics of $p$-adic mathematical physics and analysis, Tome 245 (2004), pp. 146-153. http://geodesic.mathdoc.fr/item/TM_2004_245_a14/