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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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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
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\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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This publication is cited in the following articles:
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A. Yu. Khrennikov, “Mathematical methods of non-Archimedean physics”, Russian Math. Surveys, 45:4 (1990), 87–125
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A. Yu. Khrennikov, “Quantum mechanics over non-Archimedean number fields”, Theoret. and Math. Phys., 83:3 (1990), 623–632
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A. Yu. Khrennikov, “Generalized functions on a Non-Archimedean superspace”, Math. USSR-Izv., 39:3 (1992), 1209–1238
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A. Yu. Khrennikov, “Generalized functions and Gaussian path integrals over non-archimedean function spaces”, Math. USSR-Izv., 39:1 (1992), 761–794
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A. Yu. Khrennikov, “On the theory of infinite-dimensional superspace: reflexive Banach supermodules”, Russian Acad. Sci. Sb. Math., 77:2 (1994), 331–350
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A. Yu. Khrennikov, “The infinite-dimensional Liouville equation”, Russian Acad. Sci. Sb. Math., 75:1 (1993), 17–41
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A. Yu. Khrennikov, R. Cianci, “Nonlinear evolution equations with (1,1)-supersymmetric time”, Theoret. and Math. Phys., 97:2 (1993), 1267–1272
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Roberto Cianci, Andrew Khrennikov, “Differential equations with supersymmetric time”, Lett Math Phys, 30:4 (1994), 279
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O. E. Galkin, “Infinite-dimensional superanalogs of the Mehler formula”, Math. Notes, 59:6 (1996), 671–675
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