Riesz-Martin representation for positive super-polyharmonic functions in A Riemannian manifold

V. Anandam and S. I. Othman

International Journal of Mathematics and Mathematical Sciences, 2006, vol. 2006, 1-9

Abstract:

Let u be a super-biharmonic function, that is, Δ 2 u ≥ 0 , on the unit disc D in the complex plane, satisfying certainconditions. Then it has been shown that u has a representationanalogous to the Poisson-Jensen representation for subharmonicfunctions on D . In the same vein, it is shown here that afunction u on any Green domain Ω in a Riemannianmanifold satisfying the conditions ( − Δ ) i u ≥ 0 for 0 ≤ i ≤ m has a representation analogous to the Riesz-Martinrepresentation for positive superharmonic functions on Ω .

Date: 2006
References: Add references at CitEc
Citations:

Downloads: (external link)
http://downloads.hindawi.com/journals/IJMMS/2006/092176.pdf (application/pdf)
http://downloads.hindawi.com/journals/IJMMS/2006/092176.xml (text/xml)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:092176

DOI: 10.1155/IJMMS/2006/92176

Access Statistics for this article

More articles in International Journal of Mathematics and Mathematical Sciences from Hindawi
Bibliographic data for series maintained by Mohamed Abdelhakeem ().