Polyharmonic Functions on Trees

In this paper, we introduce and study polyharmonic functions on trees. We prove that the discrete version of the classical Riquier problem can be solved on trees. Next, we show that the discrete version of a characterization of harmonic functions due to Globevnik and Rudin holds for biharmonic funct...

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Veröffentlicht in:	American journal of mathematics 2002-10, Vol.124 (5), p.999-1043
Hauptverfasser:	Cohen, Joel M., Colonna, Flavia, Gowrisankaran, Kohur, Singman, David
Format:	Artikel
Sprache:	eng
Schlagworte:	Boundary points Boundary value problems Children Dirichlet problem Exact sciences and technology Geometry Harmonic functions Integers Integral equations Martingales Mathematical analysis Mathematical functions Mathematics Partial differential equations Sciences and techniques of general use Special functions Vertices
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