Some generic fractal properties of bounded self-adjoint operators

2020/07/26 by Aloisio, Moacir, Carvalho, Silas L., de Oliveira, César R.
#FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Spectral Theory (math.SP)

paper · doi:10.48550/arxiv.2007.13162

Abstract

We study generic fractal properties of bounded self-adjoint operators through lower and upper generalized fractal dimensions of their spectral measures. Two groups of results are presented. Firstly, it is shown that the set of vectors whose associated spectral measures have lower (upper) generalized fractal dimension equal to zero (one) for every q>1 (0

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