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标题：Riesz-Martin representation for positive super-polyharmonic functions in A Riemannian manifold
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作者：V. Anandam ; S. I. Othman
期刊名称：International Journal of Mathematics and Mathematical Sciences
印刷版ISSN：0161-1712
电子版ISSN：1687-0425
出版年度：2006
卷号：2006
DOI：10.1155/IJMMS/2006/92176
出版社：Hindawi Publishing Corporation
摘要：Let u be a super-biharmonic function, that is, Δ2u≥0, on the unit disc D in the complex plane, satisfying certain conditions. Then it has been shown that u has a representation analogous to the Poisson-Jensen representation for subharmonic functions on D. In the same vein, it is shown here that a function u on any Green domain Ω in a Riemannian manifold satisfying the conditions (−Δ)iu≥0 for 0≤i≤m has a representation analogous to the Riesz-Martin representation for positive superharmonic functions on Ω.