# 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} }

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…

## One Citation

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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