2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/62383We look at invariance of a.e. boundary condition spectral behavior under perturbations, $W$, of half-line, continuum or discrete Schrödinger operators. We extend the results of del Rio, Simon, Stolz from compactly supported $W$'s to suitable short-range $W$. We also discuss invariance of the local Hausdorff dimension of spectral measures under such perturbations.25 pagesSpectral TheoryMathematical Physics34L40; 81Q10; 34E10text