Revisiting the Christ-Kiselev's multi-linear operator technique and its applications to Schrdinger operators
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abstract
We established a generalized version of the Christ-Kiselev's multi-linear operator technique to deal with the spectral theory of Schr"odinger operators. As applications, several spectral results of perturbed periodic Schr"odinger operators are obtained, including WKB solutions, sharp transitions of preservation of absolutely continuous spectra, criteria of absence of singular spectra and sharp bounds of the Hausdorff dimension of singular spectra.
