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

Abstract

We established a generalized version of the Christ-Kiselev's multi-linear operator technique to deal with the spectral theory of Schrödinger operators. As applications, several spectral results of perturbed periodic Schrödinger 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.

References in corpus (6)

• Spectral Properties of Schrödinger Operators with Decaying Potentials
• Criteria for eigenvalues embedded into the absolutely continuous spectrum of perturbed Stark type operators
• Absence of singular continuous spectrum for perturbed discrete Schrödinger operators
• Sharp spectral transition for eigenvalues embedded into the spectral bands of perturbed periodic operators
• Zeroes of the spectral density of the periodic Schroedinger operator with Wigner-von Neumann potential
• The asymptotical behaviour of embedded eigenvalues for perturbed periodic operators