Riesz-Martin representation for positive super-polyharmonic functions in A Riemannian manifold
2006 ◽
Vol 2006
◽
pp. 1-9
Keyword(s):
Letube a super-biharmonic function, that is,Δ2u≥0, on the unit discDin the complex plane, satisfying certain conditions. Then it has been shown thatuhas a representation analogous to the Poisson-Jensen representation for subharmonic functions onD. In the same vein, it is shown here that a functionuon any Green domainΩin a Riemannian manifold satisfying the conditions(−Δ)iu≥0for0≤i≤mhas a representation analogous to the Riesz-Martin representation for positive superharmonic functions onΩ.
1986 ◽
Vol 34
(3)
◽
pp. 461-472
Keyword(s):
1987 ◽
Vol 35
(3)
◽
pp. 471-479
Keyword(s):
1974 ◽
Vol 76
(3)
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pp. 511-513
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1983 ◽
Vol 26
(3)
◽
pp. 317-323
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Keyword(s):
Keyword(s):
2015 ◽
Vol 93
(2)
◽
pp. 260-271
Keyword(s):
Keyword(s):