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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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.…