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Izv. Akad. Nauk SSSR Ser. Mat., 1991, Volume 55, Issue 6, Pages 1257–1286 (Mi izv972)  

This article is cited in 4 scientific papers (total in 4 papers)

Generalized functions on a Non-Archimedean superspace

A. Yu. Khrennikov

Moscow State Institute of Electronic Technology (Technical University)

Abstract: A theory is developed for superanalytic generalized functions on a superspace over a non-Archimedean Banach superalgebra with trivial annihilator of the odd part. A Gaussian distribution and the Volkenborn distribution are introduced on the non-Archimedean superspace. Existence and uniqueness theorems are proved for the Cauchy problem for linear differential equations with variable coefficients. The Cauchy problem for non-Archimedean superdiffusion, the Schrödinger equation, and the Schrodinger equation for supersymmetric quantum mechanics on a non-Archimedean Riemann surface are considered as applications.

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English version:
Mathematics of the USSR-Izvestiya, 1992, 39:3, 1209–1238

Bibliographic databases:

UDC: 517.075.8
MSC: Primary 46S10, 46F99, 26E30; Secondary 58C50, 81T30, 30G06, 47S10
Received: 24.04.1991

Citation: A. Yu. Khrennikov, “Generalized functions on a Non-Archimedean superspace”, Izv. Akad. Nauk SSSR Ser. Mat., 55:6 (1991), 1257–1286; Math. USSR-Izv., 39:3 (1992), 1209–1238

Citation in format AMSBIB
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\by A.~Yu.~Khrennikov
\paper Generalized functions on a Non-Archimedean superspace
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\yr 1991
\vol 55
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\pages 1257--1286
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\transl
\jour Math. USSR-Izv.
\yr 1992
\vol 39
\issue 3
\pages 1209--1238
\crossref{https://doi.org/10.1070/IM1992v039n03ABEH002244}
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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. A. Yu. Khrennikov, “On the theory of infinite-dimensional superspace: reflexive Banach supermodules”, Russian Acad. Sci. Sb. Math., 77:2 (1994), 331–350  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    3. S. A. Albeverio, J. M. Bayod, C. Perez-Garsia, A. Yu. Khrennikov, R. Cianci, “Non-Archimedean analogues of orthogonal and symmetric operators”, Izv. Math., 63:6 (1999), 1063–1087  mathnet  crossref  crossref  mathscinet  zmath  isi
    4. Albeverio S., Bayod J.M., Perez-Garcia C., Cianci R., Khrennikov A., “Non-archimedean analogues of orthogonal and symmetric operators and p-adic quantization”, Acta Applicandae Mathematicae, 57:3 (1999), 205–237  crossref  mathscinet  zmath  isi  elib
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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