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

This article is cited in 1 scientific paper (total in 1 paper)

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
Received in October 2003
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  crossref  mathscinet  zmath  isi  elib  scopus
  •    . . .  Proceedings of the Steklov Institute of Mathematics
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