Topics in Harmonic Analysis on Combinatorial Graphs

Gidelew, Getnet Abebe

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Thesis/Dissertation

Date

2014

Author

Gidelew, Getnet Abebe

Advisor

Pesenson, Isaac Z.

Committee member

Berhanu, Shiferaw
Mendoza, Gerardo A.
Nowak, Krzysztof

Department

Mathematics

DOI

http://dx.doi.org/10.34944/dspace/2896

Abstract

In recent years harmonic analysis on combinatorial graphs has attracted considerable attention. The interest is stimulated in part by multiple existing and potential applications of analysis on graphs to information theory, signal analysis, image processing, computer sciences, learning theory, and astronomy. My thesis is devoted to sampling, interpolation, approximation, and multi-resolution on graphs. The results in the existing literature concern mainly with these theories on unweighted graphs. My main objective is to extend existing theories and obtain new results about sampling, interpolation, approximation, and multi-resolution on general combinatorial graphs such as directed, undirected and weighted.

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