Revisiting the Christ–Kiselev’s multi-linear operator technique and its applications to Schrödinger operators

Source abstract

Abstract Based on Christ–Kiselev’s multi-linear operator techniques, we prove several spectral results of perturbed periodic Schrödinger operators, including WKB type solutions, sharp transitions of preservation of absolutely continuous spectra, criteria of absence of singular spectra, and sharp bounds of the Hausdorff dimension of singular continuous spectra.