# Spectral Hausdorff dimensions for a class of Schrödinger operators in bounded intervals

@inproceedings{Bazo2021SpectralHD,
title={Spectral Hausdorff dimensions for a class of Schr{\"o}dinger operators in bounded intervals},
author={Vanderl{\'e}a Rodrigues Baz{\~a}o and T O Carvalho and C{\'e}sar R. de Oliveira},
year={2021}
}
• Published 13 May 2021
• Mathematics
Exact Hausdorff dimensions are computed for singular continuous components of the spectral measures of a class of Schrödinger operators in bounded intervals. 1. Main results We are interested in Hausdorff dimensional properties of spectral measures of Schrödinger operators (1.1) (Hu)(x) = − u dx2 (x) + V (x)u(x) acting in L(Ib), where Ib = [0, b], 0 < b <∞, is a bounded interval of R; our potentials V (x) are signed combs of delta distributions carefully spaced in Ib and accumulating only at b…
1 Citations
Lower bounds for fractal dimensions of spectral measures of the period doubling Schr\"odinger operator
• Mathematics
• 2020
It is shown that there exits a lower bound $\alpha>0$ to the Hausdorff dimension of the spectral measures of the one-dimensional period doubling substitution Schrodinger operator, and, generically in

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Acknowledgements Basic notation Introduction 1. General measure theory 2. Covering and differentiation 3. Invariant measures 4. Hausdorff measures and dimension 5. Other measures and dimensions 6.