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Izv. Akad. Nauk SSSR Ser. Mat., 1990, Volume 54, Issue 3, Pages 576–606 (Mi izv1087)  

This article is cited in 9 scientific papers (total in 9 papers)

Equatios on a superspace

A. Yu. Khrennikov


Abstract: The construction of a general theory of partial differential equations on a superspace is continued in the framework of functional superanalysis. Superanalogues of the spaces $\mathscr S(\mathbf R^n)$ and $\mathscr D(\mathbf R^n)$ of generalized functions are introduced; a theorem is proved on the existence of a fundamental solution for linear differential equations with constant coefficients on a superspace. In contrast to the scalar case, there exist differential operators not having fundamental solutions. Formulas are obtained for the fundamental solutions of the Laplace operator, the heat conduction operator, the Schrödinger operator, the d'Alembert operator, and the Helmholtz operator on a superspace. There is a discussion of the role of the nilpotence condition for even ghosts in a commutative superalgebra in the construction of a theory of generalized functions.

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English version:
Mathematics of the USSR-Izvestiya, 1991, 36:3, 597–627

Bibliographic databases:

UDC: 517.98
MSC: Primary 58C50, 58G30, 58C35; Secondary 58G15, 58D25, 35S05, 81G20, 83E50, 81C99
Received: 10.06.1988

Citation: A. Yu. Khrennikov, “Equatios on a superspace”, Izv. Akad. Nauk SSSR Ser. Mat., 54:3 (1990), 576–606; Math. USSR-Izv., 36:3 (1991), 597–627

Citation in format AMSBIB
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\by A.~Yu.~Khrennikov
\paper Equatios on a superspace
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1990
\vol 54
\issue 3
\pages 576--606
\mathnet{http://mi.mathnet.ru/izv1087}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1072696}
\zmath{https://zbmath.org/?q=an:0721.46027}
\adsnasa{http://adsabs.harvard.edu/cgi-bin/bib_query?1991IzMat..36..597K}
\transl
\jour Math. USSR-Izv.
\yr 1991
\vol 36
\issue 3
\pages 597--627
\crossref{https://doi.org/10.1070/IM1991v036n03ABEH002036}


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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, “Mathematical methods of non-Archimedean physics”, Russian Math. Surveys, 45:4 (1990), 87–125  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    2. A. Yu. Khrennikov, “Quantum mechanics over non-Archimedean number fields”, Theoret. and Math. Phys., 83:3 (1990), 623–632  mathnet  crossref  mathscinet  zmath  isi
    3. A. Yu. Khrennikov, “Generalized functions on a Non-Archimedean superspace”, Math. USSR-Izv., 39:3 (1992), 1209–1238  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    4. A. Yu. Khrennikov, “Generalized functions and Gaussian path integrals over non-archimedean function spaces”, Math. USSR-Izv., 39:1 (1992), 761–794  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    5. 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
    6. A. Yu. Khrennikov, “The infinite-dimensional Liouville equation”, Russian Acad. Sci. Sb. Math., 75:1 (1993), 17–41  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    7. A. Yu. Khrennikov, R. Cianci, “Nonlinear evolution equations with (1,1)-supersymmetric time”, Theoret. and Math. Phys., 97:2 (1993), 1267–1272  mathnet  crossref  mathscinet  zmath  isi
    8. Roberto Cianci, Andrew Khrennikov, “Differential equations with supersymmetric time”, Lett Math Phys, 30:4 (1994), 279  crossref  mathscinet  zmath  isi  elib
    9. O. E. Galkin, “Infinite-dimensional superanalogs of the Mehler formula”, Math. Notes, 59:6 (1996), 671–675  mathnet  crossref  crossref  mathscinet  zmath  isi
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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