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Please use this identifier to cite or link to this item: http://hdl.handle.net/123456789/18108

Title: Biharmonic extensions on trees without positive potentials
Authors: Bajunaid, Ibtesam.
singman, David.
Cohen, Joel.
Colonna, Flavia.
Keywords: biharmonic, trees, harmonic
Issue Date: 2011
Publisher: Journal of Mathematical Analysis and Applications
Abstract: Let be a tree rooted at endowed with a nearest-neighbor transition probability that yields a recurrent random walk. We show that there exists a function biharmonic off whose Laplacian has potential theoretic importance and, in addition, has the following property: Any functiononwhich is biharmonic outside a finite set has a representation, unique up to addition of a harmonic function. We obtain a characterization of the functions biharmonic outside a finite set whose Laplacian has 0 flux similar to one that holds for a function biharmonic outside a compact set in Rfor= 23, and 4 proved by Bajunaid and Anandam. Moreover, we extend the definition of flux and, under certain restrictions on the tree, we characterize the functions Biharmonic outside a finite set that have finite flux in this extended sense.
URI: http://hdl.handle.net/123456789/18108
ISSN: 0022-247x
Appears in Collections:College of Science

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