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 Tr. Mat. Inst. Steklova, 2004, Volume 245, Pages 146–153 (Mi tm180)

Construction of Interaction Measures on the Space of Distributions over the Field of $p$-Adic Numbers

A. N. Kochubei, M. R. Sait-Ametov

Institute of Mathematics, Ukrainian National Academy of Sciences

Abstract: 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.

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English version:
Proceedings of the Steklov Institute of Mathematics, 2004, 245, 135–142

Bibliographic databases:

UDC: 517.94
Language: English

Citation: A. N. Kochubei, M. R. Sait-Ametov, “Construction of Interaction Measures on the Space of Distributions over the Field of $p$-Adic Numbers”, Selected topics of $p$-adic mathematical physics and analysis, Collected papers. Dedicated to the 80th birthday of academician Vasilii Sergeevich Vladimirov, Tr. Mat. Inst. Steklova, 245, Nauka, MAIK «Nauka/Inteperiodika», M., 2004, 146–153; Proc. Steklov Inst. Math., 245 (2004), 135–142

Citation in format AMSBIB
\Bibitem{KocSai04} \by A.~N.~Kochubei, M.~R.~Sait-Ametov \paper Construction of Interaction Measures on the Space of Distributions over the Field of $p$-Adic Numbers \inbook Selected topics of $p$-adic mathematical physics and analysis \bookinfo Collected papers. Dedicated to the 80th birthday of academician Vasilii Sergeevich Vladimirov \serial Tr. Mat. Inst. Steklova \yr 2004 \vol 245 \pages 146--153 \publ Nauka, MAIK «Nauka/Inteperiodika» \publaddr M. \mathnet{http://mi.mathnet.ru/tm180} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=2099877} \zmath{https://zbmath.org/?q=an:1098.81060} \transl \jour Proc. Steklov Inst. Math. \yr 2004 \vol 245 \pages 135--142 

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This publication is cited in the following articles:
1. Torba S.M. Zuniga-Galindo W.A., “Parabolic Type Equations and Markov Stochastic Processes on Adeles”, J. Fourier Anal. Appl., 19:4 (2013), 792–835
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