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Normalized system for the super Laplace operator. (English) Zbl 1256.81054
Summary: In this paper, a 0-normalized system for the super Laplace operator (i.e., a Laplace operator in a superspace) is established. According to this system, we obtain Almansi type decomposition of polyharmonic functions in the superspace. Besides, we set up the relationship between the Riquier problem and the Dirichlet problem in the superspace. In the end, the connection between harmonic functions and solutions to the Helmholtz equation in the superspace is investigated.

MSC:
81Q60 Supersymmetry and quantum mechanics
46S60 Functional analysis on superspaces (supermanifolds) or graded spaces
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