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This article is cited in 10 scientific papers (total in 10 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.
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
Linking options:
https://www.mathnet.ru/eng/im1087https://doi.org/10.1070/IM1991v036n03ABEH002036 https://www.mathnet.ru/eng/im/v54/i3/p576
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Abstract page: | 563 | Russian version PDF: | 180 | English version PDF: | 19 | References: | 73 | First page: | 1 |
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