Frames and factorization of graph Laplacians

Frames and factorization of graph Laplacians

Using functions from electrical networks (graphs with resistors assigned to edges), we prove existence (with explicit formulas) of a canonical Parseval frame in the energy Hilbert space \(\mathscr{H}_{E}\) of a prescribed infinite (or finite) network. Outside degenerate cases, our Parseval frame is...

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Bibliographic Details
Main Authors: Palle Jorgensen, Feng Tian
Format: Article
Language:English
Published: AGH Univeristy of Science and Technology Press 2015-01-01
Series:Opuscula Mathematica
Subjects:
unbounded operators
deficiency-indices
Hilbert space
boundary values
weighted graph
reproducing kernel
Dirichlet form
graph Laplacian
resistance network
harmonic analysis
harmonic analysis, frame
Parseval frame
Friedrichs extension
reversible random walk
resistance distance
energy Hilbert space
Online Access:http://www.opuscula.agh.edu.pl/vol35/3/art/opuscula_math_3520.pdf

Internet

http://www.opuscula.agh.edu.pl/vol35/3/art/opuscula_math_3520.pdf

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