Atomic representations of Cuntz algebras
Abbreviated Journal Title
J. Math. Anal. Appl.
Iterated function system; Wavelet; Spectral measures; Cuntz algebras; Walsh bases; Permutative representations; ITERATED FUNCTION SYSTEMS; FRACTAL MEASURES; FOURIER-SERIES; WAVELETS; ENDOMORPHISMS; EXPANSIONS; ISOMETRIES; OPERATORS; STATES; SPACE; Mathematics, Applied; Mathematics
To a representation of O-N (the Cuntz algebra with N generators) we associate a projection valued measure and we study the case when this measure has atoms. The main technical tool are the spaces invariant for all the operators S. We classify the purely atomic representations and find when such representations are permutative. Applications include: wavelet representations, representations generated by finitely correlated states, representation associated to Hadamard triples (or fractal spectral measures) and representations associated to generalized Walsh bases. (C) 2014 Published by Elsevier Inc.
Journal of Mathematical Analysis and Applications
"Atomic representations of Cuntz algebras" (2015). Faculty Bibliography 2010s. 6516.