Wavelets and graph C -algebras

Carla Farsi, Elizabeth Gillaspy, Sooran Kang, Judith Packer

Research output: Chapter in Book/Report/Conference proceedingChapterpeer-review

Abstract

Here we give an overview on the connection between wavelet theory and representation theory for graph C-algebras, including the higher-rank graph C-algebras of A. Kumjian and D. Pask. Many authors have studied different aspects of this connection over the last 20 years, and we begin this paper with a survey of the known results. We then discuss several new ways to generalize these results and obtain wavelets associated to representations of higher-rank graphs. In Farsi et al. (J Math Anal Appl 425:241–270, 2015), we introduced the “cubical wavelets” associated to a higher-rank graph. Here, we generalize this construction to build wavelets of arbitrary shapes. We also present a different but related construction of wavelets associated to a higher-rank graph, which we anticipate will have applications to traffic analysis on networks. Finally, we generalize the spectral graph wavelets of Hammond et al. (Appl Comput Harmon Anal 30:129–150, 2011) to higher-rank graphs, giving a third family of wavelets associated to higher-rank graphs.

Original languageEnglish
Title of host publicationApplied and Numerical Harmonic Analysis
PublisherSpringer International Publishing
Pages35-86
Number of pages52
Edition9783319547107
DOIs
StatePublished - 2017

Publication series

NameApplied and Numerical Harmonic Analysis
Number9783319547107
ISSN (Print)2296-5009
ISSN (Electronic)2296-5017

Keywords

  • Graph wavelets
  • Higher-rank graphs
  • Representations of C-algebras

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