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Izv. Akad. Nauk SSSR Ser. Mat., 1991, Volume 55, Issue 4, Pages 780–814 (Mi izv988)  

This article is cited in 6 scientific papers (total in 6 papers)

Generalized functions and Gaussian path integrals over non-archimedean function spaces

A. Yu. Khrennikov


Abstract: A mathematical apparatus is developed for non-Archimedean physics: a theory of generalized functions, a theory of integration, and a harmonic analysis. Both finite-dimensional and infinite-dimensional non-Archimedean spaces are considered. Gaussian and Feynman path integrals on non-Archimedean function spaces are introduced. Quantization of a non-Archimedean scalar bosonic field is carried out in the formalism of path integrals. Linear differential equations in spaces of test functions and spaces of generalized functions on infinite-dimensional non-Archimedean spaces are studied (in particular, the heat equation and the Schrödinger equation with a potential).

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English version:
Mathematics of the USSR-Izvestiya, 1992, 39:1, 761–794

Bibliographic databases:

UDC: 517.948+530.1+517.2
MSC: Primary 58C50, 81S40, 46S10; Secondary 46F05, 46F12, 26E30, 81T30, 58F06, 35S05
Received: 12.10.1989

Citation: A. Yu. Khrennikov, “Generalized functions and Gaussian path integrals over non-archimedean function spaces”, Izv. Akad. Nauk SSSR Ser. Mat., 55:4 (1991), 780–814; Math. USSR-Izv., 39:1 (1992), 761–794

Citation in format AMSBIB
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\by A.~Yu.~Khrennikov
\paper Generalized functions and Gaussian path integrals over non-archimedean function spaces
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1991
\vol 55
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\pages 780--814
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\transl
\jour Math. USSR-Izv.
\yr 1992
\vol 39
\issue 1
\pages 761--794
\crossref{https://doi.org/10.1070/IM1992v039n01ABEH002225}
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. A. Yu. Khrennikov, M. Endo, “Unboundedness of a $p$-adic Gaussian distribution”, Russian Acad. Sci. Izv. Math., 41:2 (1993), 367–375  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    2. S. S. Akbarov, “Smooth structure and differential operators on a locally compact group”, Izv. Math., 59:1 (1995), 1–44  mathnet  crossref  mathscinet  zmath  isi
    3. A. Kh. Bikulov, I. V. Volovich, “$p$-adic Brownian motion”, Izv. Math., 61:3 (1997), 537–552  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    4. Youngho JANG, “Non-Archimedean quantum mechanics”, Tohoku Math Publ, 10:10 (1998), 1  crossref  mathscinet  zmath
    5. A. Yu. Khrennikov, “Laws of large numbers in non-Archimedean probability theory”, Izv. Math., 64:1 (2000), 207–219  mathnet  crossref  crossref  mathscinet  zmath  isi
    6. A. Yu. Khrennikov, H. Petersson, “A Paley–Wiener theorem for generalized entire functions on infinite-dimensional spaces”, Izv. Math., 65:2 (2001), 403–424  mathnet  crossref  crossref  mathscinet  zmath  elib
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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