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Journal of Operator Theory

Volume 88, Issue 1, Summer 2022  pp. 141-172.

Representations of Cuntz algebras associated to random walks on graphs

Authors:  Nicholas J. Christoffersen (1), Dorin Ervin Dutkay (2)
Author institution: (1) Department of Mathematics, Louisiana State University, Baton Rouge, LA 70803-4918, U.S.A.
(2) Department of Mathematics, University of Central Florida, 4000 Central Florida Blvd., P.O. Box 161364, Orlando, FL 32816-1364, U.S.A.

Summary:  Motivated by the harmonic analysis of selfaffine measures, we introduce a class of representations of the Cuntz algebra associated to random walks on graphs. The representations are constructed using the dilation theory of row coisometries. We study these representations, their commutant and the intertwining operators.

Keywords: Cuntz algebras, random walks

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