Green functions on product networks

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Cita com:
hdl:2117/132036
Document typeArticle
Defense date2018-01-01
Rights accessOpen Access
Abstract
We aim here at determining the Green function for general Schrödinger operators on product networks. The first step consists in expressing Schrödinger operators on a product network as sum of appropriate Schrödinger operators on each factor network. Hence, we apply the philosophy of the separation of variables method in PDE, to express the Green function for the Schrödinger operator on a product network using Green functions on one of the factors and the eigenvalues and eigenfunctions of some Schrödinger operator on the other factor network. We emphasize that our method only needs the knowledge of eigenvalues and eigenfunctions of one of the factors, whereas other previous works need the spectral information of both factors. We apply our results to compute the Green function of
Pm×Sh
, where
Pm
is a Path with
m
vertices and
Sh
is a Star network with
h+1
vertices.
CitationArauz, C. [et al.]. Green functions on product networks. "Discrete applied mathematics", Vol. 263, pp.22-34
ISSN0166-218X
Publisher versionhttps://www.sciencedirect.com/science/article/pii/S0166218X18305122
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