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

  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},
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… 
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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.