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Izv. RAN. Ser. Mat., 1992, Volume 56, Issue 5, Pages 1104–1115 (Mi izv921)  

This article is cited in 5 scientific papers (total in 5 papers)

Unboundedness of a $p$-adic Gaussian distribution

A. Yu. Khrennikov, M. Endo


Abstract: The intensive development of mathematical physics over non-Archimedean number fields has led to the emergence of many new mathematical constructions. In particular, a $p$-adic Gaussian distribution was introduced that lies at the basis of $p$-adic quantum mechanics with $p$-adic-valued functions. In this paper it is proved that, in contrast to the real theory, a Gaussian distribution in the $p$-adic case is not a measure, and the corresponding linear functional is unbounded on the space of continuous functions.

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English version:
Russian Academy of Sciences. Izvestiya Mathematics, 1993, 41:2, 367–375

Bibliographic databases:

UDC: 512.11
MSC: Primary 46F99; Secondary 28C20, 11S80, 11K41, 14G20, 81Q99
Received: 21.11.1991

Citation: A. Yu. Khrennikov, M. Endo, “Unboundedness of a $p$-adic Gaussian distribution”, Izv. RAN. Ser. Mat., 56:5 (1992), 1104–1115; Russian Acad. Sci. Izv. Math., 41:2 (1993), 367–375

Citation in format AMSBIB
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\paper Unboundedness of a $p$-adic Gaussian distribution
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\yr 1992
\vol 56
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\pages 1104--1115
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\adsnasa{http://adsabs.harvard.edu/cgi-bin/bib_query?1993IzMat..41..367K}
\transl
\jour Russian Acad. Sci. Izv. Math.
\yr 1993
\vol 41
\issue 2
\pages 367--375
\crossref{https://doi.org/10.1070/IM1993v041n02ABEH002266}
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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, “A limit theorem for $p$-adic-valued probability distributions”, Izv. Math., 59:3 (1995), 647–662  mathnet  crossref  mathscinet  zmath  isi
    2. Youngho JANG, “Non-Archimedean quantum mechanics”, Tohoku Math Publ, 10:10 (1998), 1  crossref  mathscinet  zmath
    3. S. V. Lyudkovskii, “Quasi-invariant and pseudo-differentiable measures with values in non-Archimedean fields on a non-Archimedean Banach space”, J. Math. Sci., 128:6 (2005), 3428–3460  mathnet  crossref  mathscinet  zmath  elib  elib
    4. S. V. Lyudkovskii, “Topological Transformation Groups of Manifolds over Non-Archimedean Fields, Their Representations, and Quasi-Invariant Measures, II”, Journal of Mathematical Sciences, 150:4 (2008), 2123–2223  mathnet  crossref  mathscinet  elib
    5. Farrukh Mukhamedov, “On the strong phase transition for the one-dimensional countable statep-adic Potts model”, J. Stat. Mech, 2014:1 (2014), P01007  crossref
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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