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Table 1 Key notation used in the proof

From: Bandlimited graph signal reconstruction by diffusion operator

Symbol Description
P w The graph frequency cut-off operator
w The graph cut-off frequency
S The downsampling set
V The set of vertices of the graph
E The set of edges connecting vertices
\({\mathcal {F}}\) The graph Fourier transform
\({{\mathcal {F}}^{- 1}}\) The inverse graph Fourier transform
P T The downsampling operator
u,v The vertex
P d The diffusion operator
f A bandlimited graph signal
P m The local-mean diffusion operator
P b The global-bias diffusion operator
K(u) The local-diffused unsampled vertices set of the sampled vertex u
d(v) The degree of the vertex v
α 1,α 2 The downsampling parameter
M The cardinality of the downsampling vertices set
N The cardinality of the graph vertices set
Y The cardinality of the eigenvalue less than the graph cut-off frequency
H K(u) The maximal distance from sampled vertex u to other vertices within K(u)
X K(u) The cardinality of K(u)
R max The maximal value of the product of X K(u) and H K(u) in graph
J(u) The degree operator of K(u)
J max The maximal value J(u) in graph